Simplify -7a^2(3a^3-4a^5)

$- 7 a^{2} (3 a^{3} - 4 a^{5})$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$- 7 a^{2} (3 a^{3}) - 7 a^{2} (- 4 a^{5})$

Reorder.

Rewrite using the commutative property of multiplication.

$- 7 \cdot 3 a^{2} a^{3} - 7 a^{2} (- 4 a^{5})$

Rewrite using the commutative property of multiplication.

$- 7 \cdot 3 a^{2} a^{3} - 7 \cdot - 4 a^{2} a^{5}$

Step 2

Simplify each term.

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

Move $a^{3}$ .

$- 7 \cdot 3 (a^{3} a^{2}) - 7 \cdot - 4 a^{2} a^{5}$

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

$- 7 \cdot 3 a^{3 + 2} - 7 \cdot - 4 a^{2} a^{5}$

Add $3$ and $2$ .

$- 7 \cdot 3 a^{5} - 7 \cdot - 4 a^{2} a^{5}$

Multiply $- 7$ by $3$ .

$- 21 a^{5} - 7 \cdot - 4 a^{2} a^{5}$

Multiply $a^{2}$ by $a^{5}$ by adding the exponents.

Move $a^{5}$ .

$- 21 a^{5} - 7 \cdot - 4 (a^{5} a^{2})$

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

$- 21 a^{5} - 7 \cdot - 4 a^{5 + 2}$

Add $5$ and $2$ .

$- 21 a^{5} - 7 \cdot - 4 a^{7}$

Multiply $- 7$ by $- 4$ .

$- 21 a^{5} + 28 a^{7}$