Algebra - ACT Math

A number that tells how many times to multiply the base by itself (in $x^3$, the exponent is 3)

$2x^2 + 7x$

$(x + 3)(x - 3)$ (difference of squares: $a^2 - b^2 = (a + b)(a - b)$)

$a(b + c) = ab + ac$ (multiply the term outside parentheses by each term inside)

$x < 7$

$2x^2 + 4x - 7$ (Distribute the negative: $4x^2 + 3x - 2 - 2x^2 + x - 5$)

$x = 6$, $y = 4$ (Add equations: $2x = 12$, so $x = 6$; substitute back: $6 + y = 10$, so $y = 4$)

A mnemonic for multiplying two binomials (just the distributive property): First, Outer, Inner, Last terms

$x = 20$

Write it as a product of simpler expressions (reverse of distributing)

$2x^2 + 9x - 5$

$5y + 4$

$x = 4$ or $x = -4$ (take square root of both sides, $\pm 4$)

An equation that can be written as $ax^2+bx+c=0$ with $a\neq 0$.

$x = 11$ (Multiply both sides by 2: $x - 3 = 8$, then $x = 11$)

$x^8/x^3=x^{8-3}=x^5$ for $x\neq 0$

Terms with the same variable(s) raised to the same power(s) (e.g., $3x$ and $5x$; $2x^2$ and $-4x^2$)

$x \geq 6$ ($2x \geq 12$, so $x \geq 6$)

$11$ ($2(3) + 5 = 6 + 5 = 11$)