Basic Math Examples

${(y + 3)}^{2} - 4 y^{2}$

Step 1

Rewrite $4 y^{2}$ as ${(2 y)}^{2}$ .

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

Step 2

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

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

Step 3

Simplify.

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Step 3.1

Add $y$ and $2 y$ .

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

Step 3.2

Factor $3$ out of $3 y + 3$ .

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Step 3.2.1

Factor $3$ out of $3 y$ .

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

Step 3.2.2

Factor $3$ out of $3$ .

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

Step 3.2.3

Factor $3$ out of $3 (y) + 3 (1)$ .

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

Step 3.3

Multiply $2$ by $- 1$ .

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

Step 4

Subtract $2 y$ from $y$ .

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

Step 5

Factor.

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Step 5.1

Factor $- 1$ out of $- y + 3$ .

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Step 5.1.1

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

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

Step 5.1.2

Rewrite $3$ as $- 1 (- 3)$ .

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

Step 5.1.3

Factor $- 1$ out of $- (y) - 1 (- 3)$ .

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

Step 5.2

Remove unnecessary parentheses.

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

Step 6

Combine exponents.

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Step 6.1

Factor out negative.

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

Step 6.2

Multiply $3$ by $- 1$ .

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

Step 7

Remove unnecessary parentheses.

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