How to find the square of difference

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ACT Math › How to find the square of difference

Questions 1 - 3

1

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

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

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

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

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

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.

Now factor the quadratic in the denominator.

Substitute these factorizations back into the original expression.

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

The terms cancel out, leaving us with the following answer:

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

2

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

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

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

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

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

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

Explanation

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

3

Expand:

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.

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