Algebra Examples

$9 y^{2} - {(1 + 2 y)}^{2}$

Step 1

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

${(3 y)}^{2} - {(1 + 2 y)}^{2}$

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 $b = 1 + 2 y$ .

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

Step 3

Simplify.

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Step 3.1

Add $3 y$ and $2 y$ .

$(5 y + 1) (3 y - (1 + 2 y))$

Step 3.2

Apply the distributive property.

$(5 y + 1) (3 y - 1 \cdot 1 - (2 y))$

Step 3.3

Multiply $- 1$ by $1$ .

$(5 y + 1) (3 y - 1 - (2 y))$

Step 3.4

Multiply $2$ by $- 1$ .

$(5 y + 1) (3 y - 1 - 2 y)$

Step 3.5

Subtract $2 y$ from $3 y$ .

$(5 y + 1) (y - 1)$