SAT Math Flashcards: Equivalent Expressions

Study Equivalent Expressions in SAT Math with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

SAT Math

Equivalent Expressions

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QUESTION

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What is the identity property of multiplication?

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ANSWER

$a \times 1 = a$ . Multiplying by 1 doesn't change the value.

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What this deck covers

This deck focuses on Equivalent Expressions, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

All flashcards

Flashcard 1: What is the identity property of multiplication?

Answer: $a \times 1 = a$ . Multiplying by 1 doesn't change the value.

Flashcard 2: Simplify: $6 - (3x + 2) + 4x$ .

Answer: $x + 4$ . Distribute negative, then combine like terms.

Flashcard 3: Simplify the expression: $2(x + 5) - 3x$ .

Answer: $-x + 10$ . Distribute 2, then combine like terms.

Flashcard 4: What is the simplified form of $2x + 3x$ ?

Answer: $5x$ . Combine like terms by adding coefficients.

Flashcard 5: What is the simplified form of $3(x + 2) - x$ ?

Answer: $2x + 6$ . Distribute 3, then combine like terms.

Flashcard 6: What is the identity property of addition?

Answer: $a + 0 = a$ . Adding zero doesn't change the value.

Flashcard 7: Simplify: $2(3a + 4) - 5a$ .

Answer: $a + 8$ . Distribute 2, then combine like terms.

Flashcard 8: Simplify the expression: $2(x + 5) - 3x$ .

Answer: $-x + 10$ . Distribute 2, then combine like terms.

Flashcard 9: What is the simplified form of $3(x + 4) + 2x$ ?

Answer: $5x + 12$ . Distribute 3, then combine like terms.

Flashcard 10: Simplify: $2(3a + 4) - 5a$ .

Answer: $a + 8$ . Distribute 2, then combine like terms.

Flashcard 11: Which expression is equivalent to $a^2 - 2ab + b^2$ ?

Answer: $(a - b)^2$ . Perfect square trinomial pattern: $a^2 - 2ab + b^2 = (a - b)^2$ .

Flashcard 12: What is the inverse property of multiplication?

Answer: $a \times \frac{1}{a} = 1$ for $a \neq 0$ . Multiplying by reciprocal gives 1.

Flashcard 13: Find the equivalent expression for $2(x - 5) + 3(x + 2)$ .

Answer: $5x - 4$ . Distribute and combine: $2x - 10 + 3x + 6 = 5x - 4$ .

Flashcard 14: Simplify: $6 - (3x + 2) + 4x$ .

Answer: $x + 4$ . Distribute negative, then combine like terms.

Flashcard 15: Which expression is equivalent to $-3(x - 2) + 4x$ ?

Answer: $x + 6$ . Distribute -3, then combine like terms.

Flashcard 16: What is the simplified form of $2x + 3(x - 1)$ ?

Answer: $5x - 3$ . Distribute 3, then combine like terms.

Flashcard 17: Simplify the expression $\frac{3x}{2} + \frac{x}{2}$ .

Answer: $2x$ . Add fractions with same denominator: $\frac{3x + x}{2} = \frac{4x}{2} = 2x$ .

Flashcard 18: Which expression is equivalent to $x(x - 3) + x$ ?

Answer: $x^2 - 2x$ . Distribute $x$ , then combine like terms.

Flashcard 19: Which expression is equivalent to $8 - (2x - 3)$ ?

Answer: $11 - 2x$ . Distribute negative sign, then combine like terms.

Flashcard 20: Simplify the expression $\frac{3x}{2} + \frac{x}{2}$ .

Answer: $2x$ . Add fractions with same denominator: $\frac{3x + x}{2} = \frac{4x}{2} = 2x$ .

Flashcard 21: State the distributive property formula.

Answer: $a(b + c) = ab + ac$ . Multiplying distributes over addition inside parentheses.

Flashcard 22: What is the simplified form of $6 - 2(3 - x)$ ?

Answer: $2x$ . Distribute -2, then combine like terms.

Flashcard 23: Simplify: $-4(a - 2) + 3a$ .

Answer: $-a + 8$ . Distribute -4, then combine like terms.

Flashcard 24: Which expression is equivalent to $4x^2 - 9$ ?

Answer: $(2x - 3)(2x + 3)$ . Difference of squares: $(2x)^2 - 3^2 = (2x - 3)(2x + 3)$ .

Flashcard 25: Which expression is equivalent to $-3(x - 2) + 4x$ ?

Answer: $x + 6$ . Distribute -3, then combine like terms.

Flashcard 26: Simplify the expression: $4(y - 3) + 2y$ .

Answer: $6y - 12$ . Distribute 4, then combine like terms.

Flashcard 27: Simplify the expression $2(x + 3) - 4x$ .

Answer: $-2x + 6$ . Distribute then combine like terms: $2x + 6 - 4x = -2x + 6$ .

Flashcard 28: Simplify the expression: $4(y - 3) + 2y$ .

Answer: $6y - 12$ . Distribute 4, then combine like terms.

Flashcard 29: What is the result of $5(2x - 1) - 3x$ ?

Answer: $7x - 5$ . Distribute 5, then combine like terms.

Flashcard 30: Simplify: $5y - 3 + 2y + 7$ .

Answer: $7y + 4$ . Group like terms and combine coefficients.

Flashcard 31: Simplify: $3(x + 2) - 4(x - 1)$ .

Answer: $-x + 10$ . Distribute both terms, then combine like terms.

Flashcard 32: Which expression is equivalent to $4x^2 - 9$ ?

Answer: $(2x - 3)(2x + 3)$ . Difference of squares: $(2x)^2 - 3^2 = (2x - 3)(2x + 3)$ .

Flashcard 33: What is the simplified expression for $7x - (2x + 3)$ ?

Answer: $5x - 3$ . Distribute negative sign, then combine like terms.

Flashcard 34: What is the simplified form of $2x + 3(x - 1)$ ?

Answer: $5x - 3$ . Distribute 3, then combine like terms.

Flashcard 35: Identify the like terms in $7x^2 + 3x - 2x^2 + 4$ .

Answer: $7x^2$ and $-2x^2$ . Like terms have the same variable and exponent.

Flashcard 36: What is the simplified form of $2x + 3x$ ?

Answer: $5x$ . Combine like terms by adding coefficients.

Flashcard 37: Identify the equivalent expression for $x^2 + 2xy + y^2$ .

Answer: $(x + y)^2$ . Perfect square trinomial pattern: $a^2 + 2ab + b^2 = (a + b)^2$ .

Flashcard 38: Simplify: $3(x + 2) - 4(x - 1)$ .

Answer: $-x + 10$ . Distribute both terms, then combine like terms.

Flashcard 39: What is the factored form of $x^2 - 4$ ?

Answer: $(x - 2)(x + 2)$ . Difference of squares: $a^2 - b^2 = (a - b)(a + b)$ .

Flashcard 40: Which expression is equivalent to $a^2 - 2ab + b^2$ ?

Answer: $(a - b)^2$ . Perfect square trinomial pattern: $a^2 - 2ab + b^2 = (a - b)^2$ .

Flashcard 41: Which expression is equivalent to $2(x + 4) + 3$ ?

Answer: $2x + 11$ . Distribute 2, then add 3.

Flashcard 42: Which expression is equivalent to $5(a + b)$ ?

Answer: $5a + 5b$ . Distribute 5 to both terms inside parentheses.

Flashcard 43: Find the equivalent expression for $2(x - 5) + 3(x + 2)$ .

Answer: $5x - 4$ . Distribute and combine: $2x - 10 + 3x + 6 = 5x - 4$ .

Flashcard 44: Simplify the expression $2(x + 3) - 4x$ .

Answer: $-2x + 6$ . Distribute then combine like terms: $2x + 6 - 4x = -2x + 6$ .

Flashcard 45: What is the simplified form of $6 - 2(3 - x)$ ?

Answer: $2x$ . Distribute -2, then combine like terms.

Flashcard 46: What is the simplified form of $3(x + 2) - x$ ?

Answer: $2x + 6$ . Distribute 3, then combine like terms.

Flashcard 47: What is the identity property of addition?

Answer: $a + 0 = a$ . Adding zero doesn't change the value.

Flashcard 48: Simplify the expression: $2(3x - 4) + 5x$ .

Answer: $11x - 8$ . Distribute 2, then combine like terms.

Flashcard 49: Which expression is equivalent to $2(x + 4) + 3$ ?

Answer: $2x + 11$ . Distribute 2, then add 3.

Flashcard 50: What is the associative property of addition?

Answer: $(a + b) + c = a + (b + c)$ . Grouping doesn't change the sum.

Flashcard 51: State the distributive property formula.

Answer: $a(b + c) = ab + ac$ . Multiplying distributes over addition inside parentheses.

Flashcard 52: Which expression is equivalent to $4(a + 2)$ ?

Answer: $4a + 8$ . Distribute 4 to both terms inside parentheses.

Flashcard 53: Simplify: $-4(a - 2) + 3a$ .

Answer: $-a + 8$ . Distribute -4, then combine like terms.

Flashcard 54: What is the simplified form of $3(x + 4) + 2x$ ?

Answer: $5x + 12$ . Distribute 3, then combine like terms.

Flashcard 55: Which expression is the simplest form of $5x - 3x + 2$ ?

Answer: $2x + 2$ . Combine like terms by adding coefficients.

Flashcard 56: Identify the like terms in $7x^2 + 3x - 2x^2 + 4$ .

Answer: $7x^2$ and $-2x^2$ . Like terms have the same variable and exponent.

Flashcard 57: What is the commutative property of multiplication?

Answer: $ab = ba$ . Order doesn't matter in multiplication.

Flashcard 58: Which expression is equivalent to $4(a + 2)$ ?

Answer: $4a + 8$ . Distribute 4 to both terms inside parentheses.

Flashcard 59: What is the simplified form of $3x + 4x$ ?

Answer: 7x. Combine like terms by adding coefficients.

Flashcard 60: What is the associative property of addition?

Answer: $(a + b) + c = a + (b + c)$ . Grouping doesn't change the sum.

Flashcard 61: Simplify: $5y - 3 + 2y + 7$ .

Answer: $7y + 4$ . Group like terms and combine coefficients.

Flashcard 62: What is the expanded form of $(3x - 2)^2$ ?

Answer: $9x^2 - 12x + 4$ . Expand using $(a - b)^2 = a^2 - 2ab + b^2$ .

Flashcard 63: What is the simplified form of $3x + 4x$ ?

Answer: 7x. Combine like terms by adding coefficients.

Flashcard 64: Which expression is equivalent to $5(a + b)$ ?

Answer: $5a + 5b$ . Distribute 5 to both terms inside parentheses.

Flashcard 65: What is the inverse property of multiplication?

Answer: $a \times \frac{1}{a} = 1$ for $a \neq 0$ . Multiplying by reciprocal gives 1.

Flashcard 66: Identify the equivalent expression for $x^2 + 2xy + y^2$ .

Answer: $(x + y)^2$ . Perfect square trinomial pattern: $a^2 + 2ab + b^2 = (a + b)^2$ .

Flashcard 67: What is the identity property of multiplication?

Answer: $a \times 1 = a$ . Multiplying by 1 doesn't change the value.

Flashcard 68: What is the expanded form of $(3x - 2)^2$ ?

Answer: $9x^2 - 12x + 4$ . Expand using $(a - b)^2 = a^2 - 2ab + b^2$ .

Flashcard 69: What is the simplified expression for $7x - (2x + 3)$ ?

Answer: $5x - 3$ . Distribute negative sign, then combine like terms.

Flashcard 70: Which expression is equivalent to $8 - (2x - 3)$ ?

Answer: $11 - 2x$ . Distribute negative sign, then combine like terms.

Flashcard 71: Which expression is the simplest form of $5x - 3x + 2$ ?

Answer: $2x + 2$ . Combine like terms by adding coefficients.

Flashcard 72: What is the factored form of $x^2 - 4$ ?

Answer: $(x - 2)(x + 2)$ . Difference of squares: $a^2 - b^2 = (a - b)(a + b)$ .

Flashcard 73: What is the commutative property of multiplication?

Answer: $ab = ba$ . Order doesn't matter in multiplication.

SAT Math Flashcards: Equivalent Expressions

Equivalent Expressions

What this deck covers

How to use these flashcards

All flashcards

Flashcard 1: What is the identity property of multiplication?

Flashcard 2: Simplify: 6−(3x+2)+4x6 - (3x + 2) + 4x6−(3x+2)+4x.

Flashcard 3: Simplify the expression: 2(x+5)−3x2(x + 5) - 3x2(x+5)−3x.

Flashcard 4: What is the simplified form of 2x+3x2x + 3x2x+3x?

Flashcard 5: What is the simplified form of 3(x+2)−x3(x + 2) - x3(x+2)−x?

Flashcard 6: What is the identity property of addition?

Flashcard 7: Simplify: 2(3a+4)−5a2(3a + 4) - 5a2(3a+4)−5a.

Flashcard 8: Simplify the expression: 2(x+5)−3x2(x + 5) - 3x2(x+5)−3x.

Flashcard 9: What is the simplified form of 3(x+4)+2x3(x + 4) + 2x3(x+4)+2x?

Flashcard 10: Simplify: 2(3a+4)−5a2(3a + 4) - 5a2(3a+4)−5a.

Flashcard 11: Which expression is equivalent to a2−2ab+b2a^2 - 2ab + b^2a2−2ab+b2?

Flashcard 12: What is the inverse property of multiplication?

Flashcard 13: Find the equivalent expression for 2(x−5)+3(x+2)2(x - 5) + 3(x + 2)2(x−5)+3(x+2).

Flashcard 14: Simplify: 6−(3x+2)+4x6 - (3x + 2) + 4x6−(3x+2)+4x.

Flashcard 15: Which expression is equivalent to −3(x−2)+4x-3(x - 2) + 4x−3(x−2)+4x?

Flashcard 16: What is the simplified form of 2x+3(x−1)2x + 3(x - 1)2x+3(x−1)?

Flashcard 17: Simplify the expression 3x2+x2\frac{3x}{2} + \frac{x}{2}23x​+2x​.

Flashcard 18: Which expression is equivalent to x(x−3)+xx(x - 3) + xx(x−3)+x?

Flashcard 19: Which expression is equivalent to 8−(2x−3)8 - (2x - 3)8−(2x−3)?

Flashcard 20: Simplify the expression 3x2+x2\frac{3x}{2} + \frac{x}{2}23x​+2x​.

Flashcard 21: State the distributive property formula.

Flashcard 22: What is the simplified form of 6−2(3−x)6 - 2(3 - x)6−2(3−x)?

Flashcard 23: Simplify: −4(a−2)+3a-4(a - 2) + 3a−4(a−2)+3a.

Flashcard 24: Which expression is equivalent to 4x2−94x^2 - 94x2−9?

Flashcard 25: Which expression is equivalent to −3(x−2)+4x-3(x - 2) + 4x−3(x−2)+4x?

Flashcard 26: Simplify the expression: 4(y−3)+2y4(y - 3) + 2y4(y−3)+2y.

Flashcard 27: Simplify the expression 2(x+3)−4x2(x + 3) - 4x2(x+3)−4x.

Flashcard 28: Simplify the expression: 4(y−3)+2y4(y - 3) + 2y4(y−3)+2y.

Flashcard 29: What is the result of 5(2x−1)−3x5(2x - 1) - 3x5(2x−1)−3x?

Flashcard 30: Simplify: 5y−3+2y+75y - 3 + 2y + 75y−3+2y+7.

Flashcard 31: Simplify: 3(x+2)−4(x−1)3(x + 2) - 4(x - 1)3(x+2)−4(x−1).

Flashcard 32: Which expression is equivalent to 4x2−94x^2 - 94x2−9?

Flashcard 33: What is the simplified expression for 7x−(2x+3)7x - (2x + 3)7x−(2x+3)?

Flashcard 34: What is the simplified form of 2x+3(x−1)2x + 3(x - 1)2x+3(x−1)?

Flashcard 35: Identify the like terms in 7x2+3x−2x2+47x^2 + 3x - 2x^2 + 47x2+3x−2x2+4.

Flashcard 36: What is the simplified form of 2x+3x2x + 3x2x+3x?

Flashcard 37: Identify the equivalent expression for x2+2xy+y2x^2 + 2xy + y^2x2+2xy+y2.

Flashcard 38: Simplify: 3(x+2)−4(x−1)3(x + 2) - 4(x - 1)3(x+2)−4(x−1).

Flashcard 39: What is the factored form of x2−4x^2 - 4x2−4?

Flashcard 40: Which expression is equivalent to a2−2ab+b2a^2 - 2ab + b^2a2−2ab+b2?

Flashcard 41: Which expression is equivalent to 2(x+4)+32(x + 4) + 32(x+4)+3?

Flashcard 42: Which expression is equivalent to 5(a+b)5(a + b)5(a+b)?

Flashcard 43: Find the equivalent expression for 2(x−5)+3(x+2)2(x - 5) + 3(x + 2)2(x−5)+3(x+2).

Flashcard 44: Simplify the expression 2(x+3)−4x2(x + 3) - 4x2(x+3)−4x.

Flashcard 45: What is the simplified form of 6−2(3−x)6 - 2(3 - x)6−2(3−x)?

Flashcard 46: What is the simplified form of 3(x+2)−x3(x + 2) - x3(x+2)−x?