Simplify 7a^3(5a^6-2b^3)

$7 a^{3} (5 a^{6} - 2 b^{3})$

Step 1

Simplify by multiplying through.

Apply the distributive property.

$7 a^{3} (5 a^{6}) + 7 a^{3} (- 2 b^{3})$

Reorder.

Rewrite using the commutative property of multiplication.

$7 \cdot 5 a^{3} a^{6} + 7 a^{3} (- 2 b^{3})$

Rewrite using the commutative property of multiplication.

$7 \cdot 5 a^{3} a^{6} + 7 \cdot - 2 a^{3} b^{3}$

Step 2

Simplify each term.

Multiply $a^{3}$ by $a^{6}$ by adding the exponents.

Move $a^{6}$ .

$7 \cdot 5 (a^{6} a^{3}) + 7 \cdot - 2 a^{3} b^{3}$

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

$7 \cdot 5 a^{6 + 3} + 7 \cdot - 2 a^{3} b^{3}$

Add $6$ and $3$ .

$7 \cdot 5 a^{9} + 7 \cdot - 2 a^{3} b^{3}$

Multiply $7$ by $5$ .

$35 a^{9} + 7 \cdot - 2 a^{3} b^{3}$

Multiply $7$ by $- 2$ .

$35 a^{9} - 14 a^{3} b^{3}$