Simplify -4x^4y(5y^4-7z+2y^2)

$- 4 x^{4} y (5 y^{4} - 7 z + 2 y^{2})$

Step 1

Apply the distributive property.

$- 4 x^{4} y (5 y^{4}) - 4 x^{4} y (- 7 z) - 4 x^{4} y (2 y^{2})$

Step 2

Simplify.

Multiply $y$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$- 4 x^{4} (y^{4} y) \cdot 5 - 4 x^{4} y (- 7 z) - 4 x^{4} y (2 y^{2})$

Multiply $y^{4}$ by $y$ .

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

$- 4 x^{4} (y^{4} y^{1}) \cdot 5 - 4 x^{4} y (- 7 z) - 4 x^{4} y (2 y^{2})$

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

$- 4 x^{4} y^{4 + 1} \cdot 5 - 4 x^{4} y (- 7 z) - 4 x^{4} y (2 y^{2})$

Add $4$ and $1$ .

$- 4 x^{4} y^{5} \cdot 5 - 4 x^{4} y (- 7 z) - 4 x^{4} y (2 y^{2})$

Multiply $- 7$ by $- 4$ .

$- 4 x^{4} y^{5} \cdot 5 + 28 x^{4} y z - 4 x^{4} y (2 y^{2})$

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

Move $y^{2}$ .

$- 4 x^{4} y^{5} \cdot 5 + 28 x^{4} y z - 4 x^{4} (y^{2} y) \cdot 2$

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

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

$- 4 x^{4} y^{5} \cdot 5 + 28 x^{4} y z - 4 x^{4} (y^{2} y^{1}) \cdot 2$

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

$- 4 x^{4} y^{5} \cdot 5 + 28 x^{4} y z - 4 x^{4} y^{2 + 1} \cdot 2$

Add $2$ and $1$ .

$- 4 x^{4} y^{5} \cdot 5 + 28 x^{4} y z - 4 x^{4} y^{3} \cdot 2$

Step 3

Simplify each term.

Multiply $5$ by $- 4$ .

$- 20 x^{4} y^{5} + 28 x^{4} y z - 4 x^{4} y^{3} \cdot 2$

Multiply $2$ by $- 4$ .

$- 20 x^{4} y^{5} + 28 x^{4} y z - 8 x^{4} y^{3}$