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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $p$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $3$ .

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

Multiply $2$ by $1$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $p$ by $p$ by adding the exponents.

Move $p$ .

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

Multiply $p$ by $p$ .

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

Multiply $4$ by $3$ .

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

Multiply $4$ by $1$ .

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

Multiply $3$ by $- 3$ .

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

Multiply $- 3$ by $1$ .

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

Simplify by adding terms.

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

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

Subtract $9 p$ from $4 p$ .

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