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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $4$ by $6$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $- 1$ .

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

Multiply $2$ by $4$ .

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

Multiply $6$ by $2$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $2$ by $2$ .

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

Simplify by adding terms.

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

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

Subtract $2 x$ from $8 x$ .

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