Simplify 2x^2(x^3y-4x^4y^2-7)

$2 x^{2} (x^{3} y - 4 x^{4} y^{2} - 7)$

Step 1

Apply the distributive property.

$2 x^{2} (x^{3} y) + 2 x^{2} (- 4 x^{4} y^{2}) + 2 x^{2} \cdot - 7$

Step 2

Simplify.

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

Move $x^{3}$ .

$2 (x^{3} x^{2}) y + 2 x^{2} (- 4 x^{4} y^{2}) + 2 x^{2} \cdot - 7$

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

$2 x^{3 + 2} y + 2 x^{2} (- 4 x^{4} y^{2}) + 2 x^{2} \cdot - 7$

Add $3$ and $2$ .

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

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

Move $x^{4}$ .

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

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

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

Add $4$ and $2$ .

$2 x^{5} y + 2 x^{6} (- 4 y^{2}) + 2 x^{2} \cdot - 7$

Multiply $- 7$ by $2$ .

$2 x^{5} y + 2 x^{6} (- 4 y^{2}) - 14 x^{2}$

Step 3

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 x^{5} y + 2 \cdot - 4 x^{6} y^{2} - 14 x^{2}$

Multiply $2$ by $- 4$ .

$2 x^{5} y - 8 x^{6} y^{2} - 14 x^{2}$

Step 4

Reorder $2 x^{5} y$ and $- 8 x^{6} y^{2}$ .

$- 8 x^{6} y^{2} + 2 x^{5} y - 14 x^{2}$