Simplify 5a^2(3a^4+3b+2)

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $5$ .

$5 \cdot 3 a^{2} a^{4} + 5 \cdot 3 a^{2} b + 10 a^{2}$

Step 3

Simplify each term.

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

Move $a^{4}$ .

$5 \cdot 3 (a^{4} a^{2}) + 5 \cdot 3 a^{2} b + 10 a^{2}$

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

$5 \cdot 3 a^{4 + 2} + 5 \cdot 3 a^{2} b + 10 a^{2}$

Add $4$ and $2$ .

$5 \cdot 3 a^{6} + 5 \cdot 3 a^{2} b + 10 a^{2}$

Multiply $5$ by $3$ .

$15 a^{6} + 5 \cdot 3 a^{2} b + 10 a^{2}$

Multiply $5$ by $3$ .

$15 a^{6} + 15 a^{2} b + 10 a^{2}$