Find the Product -2x^a(-4x^b-2x^3+5x)

$- 2 x^{a} (- 4 x^{b} - 2 x^{3} + 5 x)$

Step 1

Apply the distributive property.

$- 2 x^{a} (- 4 x^{b}) - 2 x^{a} (- 2 x^{3}) - 2 x^{a} (5 x)$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 4 x^{a} x^{b} - 2 x^{a} (- 2 x^{3}) - 2 x^{a} (5 x)$

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 4 x^{a} x^{b} - 2 \cdot - 2 x^{a} x^{3} - 2 x^{a} (5 x)$

Rewrite using the commutative property of multiplication.

$- 2 \cdot - 4 x^{a} x^{b} - 2 \cdot - 2 x^{a} x^{3} - 2 \cdot 5 x^{a} x$

Step 3

Simplify each term.

Multiply $x^{a}$ by $x^{b}$ by adding the exponents.

Move $x^{b}$ .

$- 2 \cdot - 4 (x^{b} x^{a}) - 2 \cdot - 2 x^{a} x^{3} - 2 \cdot 5 x^{a} x$

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

$- 2 \cdot - 4 x^{b + a} - 2 \cdot - 2 x^{a} x^{3} - 2 \cdot 5 x^{a} x$

Multiply $- 2$ by $- 4$ .

$8 x^{b + a} - 2 \cdot - 2 x^{a} x^{3} - 2 \cdot 5 x^{a} x$

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

Move $x^{3}$ .

$8 x^{b + a} - 2 \cdot - 2 (x^{3} x^{a}) - 2 \cdot 5 x^{a} x$

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

$8 x^{b + a} - 2 \cdot - 2 x^{3 + a} - 2 \cdot 5 x^{a} x$

Multiply $- 2$ by $- 2$ .

$8 x^{b + a} + 4 x^{3 + a} - 2 \cdot 5 x^{a} x$

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

Move $x$ .

$8 x^{b + a} + 4 x^{3 + a} - 2 \cdot 5 (x \cdot x^{a})$

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

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

$8 x^{b + a} + 4 x^{3 + a} - 2 \cdot 5 (x^{1} x^{a})$

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

$8 x^{b + a} + 4 x^{3 + a} - 2 \cdot 5 x^{1 + a}$

Multiply $- 2$ by $5$ .

$8 x^{b + a} + 4 x^{3 + a} - 10 x^{1 + a}$