Find the Product (4s+2)(5s^2+10s+3)

$(4 s + 2) (5 s^{2} + 10 s + 3)$

Step 1

Expand $(4 s + 2) (5 s^{2} + 10 s + 3)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $s$ by $s^{2}$ by adding the exponents.

Move $s^{2}$ .

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

Multiply $s^{2}$ by $s$ .

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

$4 \cdot 5 (s^{2} s^{1}) + 4 s (10 s) + 4 s \cdot 3 + 2 (5 s^{2}) + 2 (10 s) + 2 \cdot 3$

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

$4 \cdot 5 s^{2 + 1} + 4 s (10 s) + 4 s \cdot 3 + 2 (5 s^{2}) + 2 (10 s) + 2 \cdot 3$

Add $2$ and $1$ .

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

Multiply $4$ by $5$ .

$20 s^{3} + 4 s (10 s) + 4 s \cdot 3 + 2 (5 s^{2}) + 2 (10 s) + 2 \cdot 3$

Rewrite using the commutative property of multiplication.

$20 s^{3} + 4 \cdot 10 s \cdot s + 4 s \cdot 3 + 2 (5 s^{2}) + 2 (10 s) + 2 \cdot 3$

Multiply $s$ by $s$ by adding the exponents.

Move $s$ .

$20 s^{3} + 4 \cdot 10 (s \cdot s) + 4 s \cdot 3 + 2 (5 s^{2}) + 2 (10 s) + 2 \cdot 3$

Multiply $s$ by $s$ .

$20 s^{3} + 4 \cdot 10 s^{2} + 4 s \cdot 3 + 2 (5 s^{2}) + 2 (10 s) + 2 \cdot 3$

Multiply $4$ by $10$ .

$20 s^{3} + 40 s^{2} + 4 s \cdot 3 + 2 (5 s^{2}) + 2 (10 s) + 2 \cdot 3$

Multiply $3$ by $4$ .

$20 s^{3} + 40 s^{2} + 12 s + 2 (5 s^{2}) + 2 (10 s) + 2 \cdot 3$

Multiply $5$ by $2$ .

$20 s^{3} + 40 s^{2} + 12 s + 10 s^{2} + 2 (10 s) + 2 \cdot 3$

Multiply $10$ by $2$ .

$20 s^{3} + 40 s^{2} + 12 s + 10 s^{2} + 20 s + 2 \cdot 3$

Multiply $2$ by $3$ .

$20 s^{3} + 40 s^{2} + 12 s + 10 s^{2} + 20 s + 6$

Simplify by adding terms.

Add $40 s^{2}$ and $10 s^{2}$ .

$20 s^{3} + 50 s^{2} + 12 s + 20 s + 6$

Add $12 s$ and $20 s$ .

$20 s^{3} + 50 s^{2} + 32 s + 6$