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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $a^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $4$ by $6$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $4$ by $- 1$ .

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

Multiply $2$ by $4$ .

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

Multiply $6$ by $2$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $2$ by $2$ .

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

Simplify by adding terms.

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

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

Subtract $2 a$ from $8 a$ .

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