Simplify (4s+2)(6s^2-s+2)

$(4 s + 2) (6 s^{2} - s + 2)$

Step 1

Expand $(4 s + 2) (6 s^{2} - s + 2)$ by multiplying each term in the first expression by each term in the second expression.

$4 s (6 s^{2}) + 4 s (- s) + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 6 s \cdot s^{2} + 4 s (- s) + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

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

Move $s^{2}$ .

$4 \cdot 6 (s^{2} s) + 4 s (- s) + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

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

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

$4 \cdot 6 (s^{2} s^{1}) + 4 s (- s) + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

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

$4 \cdot 6 s^{2 + 1} + 4 s (- s) + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

Add $2$ and $1$ .

$4 \cdot 6 s^{3} + 4 s (- s) + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

Multiply $4$ by $6$ .

$24 s^{3} + 4 s (- s) + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

Rewrite using the commutative property of multiplication.

$24 s^{3} + 4 \cdot - 1 s \cdot s + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

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

Move $s$ .

$24 s^{3} + 4 \cdot - 1 (s \cdot s) + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

Multiply $s$ by $s$ .

$24 s^{3} + 4 \cdot - 1 s^{2} + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

Multiply $4$ by $- 1$ .

$24 s^{3} - 4 s^{2} + 4 s \cdot 2 + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

Multiply $2$ by $4$ .

$24 s^{3} - 4 s^{2} + 8 s + 2 (6 s^{2}) + 2 (- s) + 2 \cdot 2$

Multiply $6$ by $2$ .

$24 s^{3} - 4 s^{2} + 8 s + 12 s^{2} + 2 (- s) + 2 \cdot 2$

Multiply $- 1$ by $2$ .

$24 s^{3} - 4 s^{2} + 8 s + 12 s^{2} - 2 s + 2 \cdot 2$

Multiply $2$ by $2$ .

$24 s^{3} - 4 s^{2} + 8 s + 12 s^{2} - 2 s + 4$

Simplify by adding terms.

Add $- 4 s^{2}$ and $12 s^{2}$ .

$24 s^{3} + 8 s^{2} + 8 s - 2 s + 4$

Subtract $2 s$ from $8 s$ .

$24 s^{3} + 8 s^{2} + 6 s + 4$