Simplify (2p+7)(3p^2+4p-3)

$(2 p + 7) (3 p^{2} + 4 p - 3)$

Step 1

Expand $(2 p + 7) (3 p^{2} + 4 p - 3)$ by multiplying each term in the first expression by each term in the second expression.

$2 p (3 p^{2}) + 2 p (4 p) + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 3 p \cdot p^{2} + 2 p (4 p) + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

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

Move $p^{2}$ .

$2 \cdot 3 (p^{2} p) + 2 p (4 p) + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

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

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

$2 \cdot 3 (p^{2} p^{1}) + 2 p (4 p) + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

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

$2 \cdot 3 p^{2 + 1} + 2 p (4 p) + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

Add $2$ and $1$ .

$2 \cdot 3 p^{3} + 2 p (4 p) + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

Multiply $2$ by $3$ .

$6 p^{3} + 2 p (4 p) + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

Rewrite using the commutative property of multiplication.

$6 p^{3} + 2 \cdot 4 p \cdot p + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

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

Move $p$ .

$6 p^{3} + 2 \cdot 4 (p \cdot p) + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

Multiply $p$ by $p$ .

$6 p^{3} + 2 \cdot 4 p^{2} + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

Multiply $2$ by $4$ .

$6 p^{3} + 8 p^{2} + 2 p \cdot - 3 + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

Multiply $- 3$ by $2$ .

$6 p^{3} + 8 p^{2} - 6 p + 7 (3 p^{2}) + 7 (4 p) + 7 \cdot - 3$

Multiply $3$ by $7$ .

$6 p^{3} + 8 p^{2} - 6 p + 21 p^{2} + 7 (4 p) + 7 \cdot - 3$

Multiply $4$ by $7$ .

$6 p^{3} + 8 p^{2} - 6 p + 21 p^{2} + 28 p + 7 \cdot - 3$

Multiply $7$ by $- 3$ .

$6 p^{3} + 8 p^{2} - 6 p + 21 p^{2} + 28 p - 21$

Simplify by adding terms.

Add $8 p^{2}$ and $21 p^{2}$ .

$6 p^{3} + 29 p^{2} - 6 p + 28 p - 21$

Add $- 6 p$ and $28 p$ .

$6 p^{3} + 29 p^{2} + 22 p - 21$