Factor y^2(y-4)+5(4-y)

$y^{2} (y - 4) + 5 (4 - y)$

Step 1

Apply the distributive property.

$y^{2} y + y^{2} \cdot - 4 + 5 (4 - y)$

Step 2

Multiply $y^{2}$ by $y$ by adding the exponents.

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$y^{2} y^{1} + y^{2} \cdot - 4 + 5 (4 - y)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y^{2 + 1} + y^{2} \cdot - 4 + 5 (4 - y)$

Add $2$ and $1$ .

$y^{3} + y^{2} \cdot - 4 + 5 (4 - y)$

Step 3

Move $- 4$ to the left of $y^{2}$ .

$y^{3} - 4 y^{2} + 5 (4 - y)$

Step 4

Apply the distributive property.

$y^{3} - 4 y^{2} + 5 \cdot 4 + 5 (- y)$

Step 5

Multiply $5$ by $4$ .

$y^{3} - 4 y^{2} + 20 + 5 (- y)$

Step 6

Multiply $- 1$ by $5$ .

$y^{3} - 4 y^{2} + 20 - 5 y$

Step 7

Reorder terms.

$y^{3} - 4 y^{2} - 5 y + 20$

Step 8

Rewrite $y^{3} - 4 y^{2} - 5 y + 20$ in a factored form.

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(y^{3} - 4 y^{2}) - 5 y + 20$

Factor out the greatest common factor (GCF) from each group.

$y^{2} (y - 4) - 5 (y - 4)$

Factor the polynomial by factoring out the greatest common factor, $y - 4$ .

$(y - 4) (y^{2} - 5)$