Precalculus Examples

$9 y^{4} {(y + 6)}^{3} + y^{5} {(y + 6)}^{4}$

Step 1

Factor $y^{4} {(y + 6)}^{3}$ out of $9 y^{4} {(y + 6)}^{3} + y^{5} {(y + 6)}^{4}$ .

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Step 1.1

Factor $y^{4} {(y + 6)}^{3}$ out of $9 y^{4} {(y + 6)}^{3}$ .

$y^{4} {(y + 6)}^{3} (9) + y^{5} {(y + 6)}^{4}$

Step 1.2

Factor $y^{4} {(y + 6)}^{3}$ out of $y^{5} {(y + 6)}^{4}$ .

$y^{4} {(y + 6)}^{3} (9) + y^{4} {(y + 6)}^{3} (y (y + 6))$

Step 1.3

Factor $y^{4} {(y + 6)}^{3}$ out of $y^{4} {(y + 6)}^{3} (9) + y^{4} {(y + 6)}^{3} (y (y + 6))$ .

$y^{4} {(y + 6)}^{3} (9 + y (y + 6))$

Step 2

Apply the distributive property.

$y^{4} {(y + 6)}^{3} (9 + y \cdot y + y \cdot 6)$

Step 3

Multiply $y$ by $y$ .

$y^{4} {(y + 6)}^{3} (9 + y^{2} + y \cdot 6)$

Step 4

Move $6$ to the left of $y$ .

$y^{4} {(y + 6)}^{3} (9 + y^{2} + 6 y)$

Step 5

Reorder terms.

$y^{4} {(y + 6)}^{3} (y^{2} + 6 y + 9)$

Step 6

Factor using the perfect square rule.

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Step 6.1

Rewrite $9$ as $3^{2}$ .

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

Step 6.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 y = 2 \cdot y \cdot 3$

Step 6.3

Rewrite the polynomial.

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

Step 6.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = y$ and $b = 3$ .

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