Simplify (2x^2+4x-3)(3x+1)

$(2 x^{2} + 4 x - 3) (3 x + 1)$

Step 1

Expand $(2 x^{2} + 4 x - 3) (3 x + 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $3$ .

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

Multiply $2$ by $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $4$ by $3$ .

$6 x^{3} + 2 x^{2} + 12 x^{2} + 4 x \cdot 1 - 3 (3 x) - 3 \cdot 1$

Multiply $4$ by $1$ .

$6 x^{3} + 2 x^{2} + 12 x^{2} + 4 x - 3 (3 x) - 3 \cdot 1$

Multiply $3$ by $- 3$ .

$6 x^{3} + 2 x^{2} + 12 x^{2} + 4 x - 9 x - 3 \cdot 1$

Multiply $- 3$ by $1$ .

$6 x^{3} + 2 x^{2} + 12 x^{2} + 4 x - 9 x - 3$

Simplify by adding terms.

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

$6 x^{3} + 14 x^{2} + 4 x - 9 x - 3$

Subtract $9 x$ from $4 x$ .

$6 x^{3} + 14 x^{2} - 5 x - 3$