Pre-Algebra Examples

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

Step 1

Rewrite $9 y^{2}$ as ${(3 y)}^{2}$ .

${(3 y)}^{2} - {(2 x - y)}^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3 y$ and $b = 2 x - y$ .

$(3 y + 2 x - y) (3 y - (2 x - y))$

Step 3

Simplify.

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Step 3.1

Subtract $y$ from $3 y$ .

$(2 x + 2 y) (3 y - (2 x - y))$

Step 3.2

Factor $2$ out of $2 x + 2 y$ .

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Step 3.2.1

Factor $2$ out of $2 x$ .

$(2 (x) + 2 y) (3 y - (2 x - y))$

Step 3.2.2

Factor $2$ out of $2 y$ .

$(2 (x) + 2 (y)) (3 y - (2 x - y))$

Step 3.2.3

Factor $2$ out of $2 (x) + 2 (y)$ .

$2 (x + y) (3 y - (2 x - y))$

Step 3.3

Apply the distributive property.

$2 (x + y) (3 y - (2 x) - - y)$

Step 3.4

Multiply $2$ by $- 1$ .

$2 (x + y) (3 y - 2 x - - y)$

Step 3.5

Multiply $- - y$ .

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Step 3.5.1

Multiply $- 1$ by $- 1$ .

$2 (x + y) (3 y - 2 x + 1 y)$

Step 3.5.2

Multiply $y$ by $1$ .

$2 (x + y) (3 y - 2 x + y)$

Step 3.6

Add $3 y$ and $y$ .

$2 (x + y) (- 2 x + 4 y)$

Step 3.7

Factor.

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Step 3.7.1

Factor $2$ out of $- 2 x + 4 y$ .

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Step 3.7.1.1

Factor $2$ out of $- 2 x$ .

$2 (x + y) (2 (- x) + 4 y)$

Step 3.7.1.2

Factor $2$ out of $4 y$ .

$2 (x + y) (2 (- x) + 2 (2 y))$

Step 3.7.1.3

Factor $2$ out of $2 (- x) + 2 (2 y)$ .

$2 (x + y) (2 (- x + 2 y))$

Step 3.7.2

Remove unnecessary parentheses.

$2 (x + y) \cdot 2 (- x + 2 y)$

Step 3.8

Multiply $2$ by $2$ .

$4 (x + y) (- x + 2 y)$

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $- x + 2 y$ .

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Step 4.1.1

Factor $- 1$ out of $- x$ .

$4 (x + y) (- (x) + 2 y)$

Step 4.1.2

Factor $- 1$ out of $2 y$ .

$4 (x + y) (- (x) - (- 2 y))$

Step 4.1.3

Factor $- 1$ out of $- (x) - (- 2 y)$ .

$4 (x + y) (- (x - 2 y))$

Step 4.2

Remove unnecessary parentheses.

$4 (x + y) \cdot - 1 (x - 2 y)$

Step 5

Combine exponents.

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Step 5.1

Factor out negative.

$- (4 (x + y) (x - 2 y))$

Step 5.2

Multiply $4$ by $- 1$ .

$- 4 ((x + y) (x - 2 y))$

Step 6

Remove unnecessary parentheses.

$- 4 (x + y) (x - 2 y)$