Precalculus Examples

${(5 x + 9 y)}^{2} - {(5 x - 9 y)}^{2}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 5 x + 9 y$ and $b = 5 x - 9 y$ .

$(5 x + 9 y + 5 x - 9 y) (5 x + 9 y - (5 x - 9 y))$

Step 2

Simplify.

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Step 2.1

Add $5 x$ and $5 x$ .

$(10 x + 9 y - 9 y) (5 x + 9 y - (5 x - 9 y))$

Step 2.2

Subtract $9 y$ from $9 y$ .

$(10 x + 0) (5 x + 9 y - (5 x - 9 y))$

Step 2.3

Add $10 x$ and $0$ .

$10 x (5 x + 9 y - (5 x - 9 y))$

Step 2.4

Apply the distributive property.

$10 x (5 x + 9 y - (5 x) - (- 9 y))$

Step 2.5

Multiply $5$ by $- 1$ .

$10 x (5 x + 9 y - 5 x - (- 9 y))$

Step 2.6

Multiply $- 9$ by $- 1$ .

$10 x (5 x + 9 y - 5 x + 9 y)$

Step 2.7

Subtract $5 x$ from $5 x$ .

$10 x (9 y + 0 + 9 y)$

Step 2.8

Add $9 y$ and $0$ .

$10 x (9 y + 9 y)$

Step 2.9

Factor.

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Step 2.9.1

Add $9 y$ and $9 y$ .

$10 x (18 y)$

Step 2.9.2

Remove unnecessary parentheses.

$10 x \cdot 18 y$

Step 2.10

Multiply $18$ by $10$ .

$180 x y$