Simplify 4y^2(9y^3+8y^2-11)

$4 y^{2} (9 y^{3} + 8 y^{2} - 11)$

Step 1

Apply the distributive property.

$4 y^{2} (9 y^{3}) + 4 y^{2} (8 y^{2}) + 4 y^{2} \cdot - 11$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$4 \cdot 9 y^{2} y^{3} + 4 y^{2} (8 y^{2}) + 4 y^{2} \cdot - 11$

Rewrite using the commutative property of multiplication.

$4 \cdot 9 y^{2} y^{3} + 4 \cdot 8 y^{2} y^{2} + 4 y^{2} \cdot - 11$

Multiply $- 11$ by $4$ .

$4 \cdot 9 y^{2} y^{3} + 4 \cdot 8 y^{2} y^{2} - 44 y^{2}$

Step 3

Simplify each term.

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$4 \cdot 9 (y^{3} y^{2}) + 4 \cdot 8 y^{2} y^{2} - 44 y^{2}$

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

$4 \cdot 9 y^{3 + 2} + 4 \cdot 8 y^{2} y^{2} - 44 y^{2}$

Add $3$ and $2$ .

$4 \cdot 9 y^{5} + 4 \cdot 8 y^{2} y^{2} - 44 y^{2}$

Multiply $4$ by $9$ .

$36 y^{5} + 4 \cdot 8 y^{2} y^{2} - 44 y^{2}$

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

Move $y^{2}$ .

$36 y^{5} + 4 \cdot 8 (y^{2} y^{2}) - 44 y^{2}$

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

$36 y^{5} + 4 \cdot 8 y^{2 + 2} - 44 y^{2}$

Add $2$ and $2$ .

$36 y^{5} + 4 \cdot 8 y^{4} - 44 y^{2}$

Multiply $4$ by $8$ .

$36 y^{5} + 32 y^{4} - 44 y^{2}$