Simplify (4x)^2*(2x+5y)

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

Step 1

Simplify by multiplying through.

Apply the product rule to $4 x$ .

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

Raise $4$ to the power of $2$ .

$16 x^{2} \cdot (2 x + 5 y)$

Apply the distributive property.

$16 x^{2} (2 x) + 16 x^{2} (5 y)$

Reorder.

Rewrite using the commutative property of multiplication.

$16 \cdot 2 x^{2} x + 16 x^{2} (5 y)$

Rewrite using the commutative property of multiplication.

$16 \cdot 2 x^{2} x + 16 \cdot 5 x^{2} y$

Step 2

Simplify each term.

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

Move $x$ .

$16 \cdot 2 (x \cdot x^{2}) + 16 \cdot 5 x^{2} y$

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

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

$16 \cdot 2 (x^{1} x^{2}) + 16 \cdot 5 x^{2} y$

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

$16 \cdot 2 x^{1 + 2} + 16 \cdot 5 x^{2} y$

Add $1$ and $2$ .

$16 \cdot 2 x^{3} + 16 \cdot 5 x^{2} y$

Multiply $16$ by $2$ .

$32 x^{3} + 16 \cdot 5 x^{2} y$

Multiply $16$ by $5$ .

$32 x^{3} + 80 x^{2} y$