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ACT Math : Square of Difference

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Example Questions

Example Question #1 : Square Of Difference

$\small (3a-2b)^{2}$ $\displaystyle \small (3a-2b)^{2}$ can be rewritten as:

Possible Answers:

$\small 9a^{2}+4b^{2}$ $\displaystyle \small 9a^{2}+4b^{2}$

$\small 9a^{2}-6ab+4b^{2}$ $\displaystyle \small 9a^{2}-6ab+4b^{2}$

$\small 9a^{2}-12ab+4b^{2}$ $\displaystyle \small 9a^{2}-12ab+4b^{2}$

$\small 9a^{2}-4b^{2}$ $\displaystyle \small 9a^{2}-4b^{2}$

$\small 9a^{2}+12ab+4b^{2}$ $\displaystyle \small 9a^{2}+12ab+4b^{2}$

Correct answer:

$\small 9a^{2}-12ab+4b^{2}$ $\displaystyle \small 9a^{2}-12ab+4b^{2}$

Explanation:

Use the formula for solving the square of a difference, $\small (x-y)^{2}=x^{2}-2xy+y^{2}$ $\displaystyle \small (x-y)^{2}=x^{2}-2xy+y^{2}$ . In this case, $\small \small \small (3a-2b)^{2}=9a^{2}-12ab+4b^{2}$ $\displaystyle \small \small \small (3a-2b)^{2}=9a^{2}-12ab+4b^{2}$

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Example Question #2 : Square Of Difference

Expand:

$\displaystyle (2x-6)^2$

Possible Answers:

$\displaystyle 2x^2-12x+24$

$\displaystyle 4x^2-24x+36$

4x-12 $\displaystyle 4x-12$

$\displaystyle 4x^2-12x+36$

Correct answer:

$\displaystyle 4x^2-24x+36$

Explanation:

To multiply a difference squared, square the first term and add two times the multiplication of the two terms. Then add the second term squared.

$\displaystyle (2x^)^2+2(2x)(-6)+(-6)^2=4x^2-24x+36$

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Example Question #3 : Square Of Difference

The expression $\frac{x^2-25}{x^2+11x+30}$ $\displaystyle \frac{x^2-25}{x^2+11x+30}$ is equivalent to:

Possible Answers:

x+6 $\displaystyle x+6$

$\frac{x-5}{x+6}$ $\displaystyle \frac{x-5}{x+6}$

$\frac{x+6}{x+5}$ $\displaystyle \frac{x+6}{x+5}$

$\frac{x-6}{x-5}$ $\displaystyle \frac{x-6}{x-5}$

$\frac{x+5}{x-6}$ $\displaystyle \frac{x+5}{x-6}$

Correct answer:

$\frac{x-5}{x+6}$ $\displaystyle \frac{x-5}{x+6}$

Explanation:

First, we need to factor the numerator and denominator separately and cancel out similar terms. We will start with the numerator because it can be factored easily as the difference of two squares.

$\displaystyle x^2 - 25 = (x + 5)(x - 5)$

Now factor the quadratic in the denominator.

$\displaystyle x^2 + 11x + 30 = (x + 5)(x + 6)$

Substitute these factorizations back into the original expression.

$\frac{(x+5)(x-5)}{(x+5)(x+6)}$ $\displaystyle \frac{(x+5)(x-5)}{(x+5)(x+6)}$

The (x+5) $\displaystyle (x+5)$ terms cancel out, leaving us with the following answer:

$\frac{x-5}{x+6}$ $\displaystyle \frac{x-5}{x+6}$

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ACT Math : Square of Difference

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Square Of Difference

Example Question #2 : Square Of Difference

Example Question #3 : Square Of Difference

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