Pre-Algebra Examples

$(4 y^{2} + 4 y - 24) \div (y + 3)$

Step 1

Rewrite the division as a fraction.

$\frac{4 y^{2} + 4 y - 24}{y + 3}$

Step 2

Simplify the numerator.

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Step 2.1

Factor $4$ out of $4 y^{2} + 4 y - 24$ .

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Step 2.1.1

Factor $4$ out of $4 y^{2}$ .

$\frac{4 (y^{2}) + 4 y - 24}{y + 3}$

Step 2.1.2

Factor $4$ out of $4 y$ .

$\frac{4 (y^{2}) + 4 (y) - 24}{y + 3}$

Step 2.1.3

Factor $4$ out of $- 24$ .

$\frac{4 (y^{2}) + 4 y + 4 \cdot - 6}{y + 3}$

Step 2.1.4

Factor $4$ out of $4 (y^{2}) + 4 y$ .

$\frac{4 (y^{2} + y) + 4 \cdot - 6}{y + 3}$

Step 2.1.5

Factor $4$ out of $4 (y^{2} + y) + 4 \cdot - 6$ .

$\frac{4 (y^{2} + y - 6)}{y + 3}$

Step 2.2

Factor $y^{2} + y - 6$ using the AC method.

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Step 2.2.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $1$ .

$- 2, 3$

Step 2.2.2

Write the factored form using these integers.

$\frac{4 ((y - 2) (y + 3))}{y + 3}$

$\frac{4 (y - 2) (y + 3)}{y + 3}$

Step 3

Cancel the common factor of $y + 3$ .

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Step 3.1

Cancel the common factor.

$\frac{4 (y - 2) (y + 3)}{y + 3}$

Step 3.2

Divide $4 (y - 2)$ by $1$ .

$4 (y - 2)$

Step 4

Apply the distributive property.

$4 y + 4 \cdot - 2$

Step 5

Multiply $4$ by $- 2$ .

$4 y - 8$