Simplify 4x^2y(2x^4-6xy+2)

$4 x^{2} y (2 x^{4} - 6 x y + 2)$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

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

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

Add $4$ and $2$ .

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

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

Move $x$ .

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

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

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

$4 x^{6} y \cdot 2 + 4 (x^{1} x^{2}) y (- 6 y) + 4 x^{2} y \cdot 2$

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

$4 x^{6} y \cdot 2 + 4 x^{1 + 2} y (- 6 y) + 4 x^{2} y \cdot 2$

Add $1$ and $2$ .

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

Multiply $2$ by $4$ .

$4 x^{6} y \cdot 2 + 4 x^{3} y (- 6 y) + 8 x^{2} y$

Step 3

Simplify each term.

Multiply $2$ by $4$ .

$8 x^{6} y + 4 x^{3} y (- 6 y) + 8 x^{2} y$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$8 x^{6} y + 4 x^{3} (y \cdot y) \cdot - 6 + 8 x^{2} y$

Multiply $y$ by $y$ .

$8 x^{6} y + 4 x^{3} y^{2} \cdot - 6 + 8 x^{2} y$

Multiply $- 6$ by $4$ .

$8 x^{6} y - 24 x^{3} y^{2} + 8 x^{2} y$