Simplify (3m+4)(m^2-3m+5)

$(3 m + 4) (m^{2} - 3 m + 5)$

Step 1

Expand $(3 m + 4) (m^{2} - 3 m + 5)$ by multiplying each term in the first expression by each term in the second expression.

$3 m \cdot m^{2} + 3 m (- 3 m) + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

Step 2

Simplify terms.

Simplify each term.

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

Move $m^{2}$ .

$3 (m^{2} m) + 3 m (- 3 m) + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

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

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

$3 (m^{2} m^{1}) + 3 m (- 3 m) + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

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

$3 m^{2 + 1} + 3 m (- 3 m) + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

Add $2$ and $1$ .

$3 m^{3} + 3 m (- 3 m) + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

Rewrite using the commutative property of multiplication.

$3 m^{3} + 3 \cdot - 3 m \cdot m + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$3 m^{3} + 3 \cdot - 3 (m \cdot m) + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

Multiply $m$ by $m$ .

$3 m^{3} + 3 \cdot - 3 m^{2} + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

Multiply $3$ by $- 3$ .

$3 m^{3} - 9 m^{2} + 3 m \cdot 5 + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

Multiply $5$ by $3$ .

$3 m^{3} - 9 m^{2} + 15 m + 4 m^{2} + 4 (- 3 m) + 4 \cdot 5$

Multiply $- 3$ by $4$ .

$3 m^{3} - 9 m^{2} + 15 m + 4 m^{2} - 12 m + 4 \cdot 5$

Multiply $4$ by $5$ .

$3 m^{3} - 9 m^{2} + 15 m + 4 m^{2} - 12 m + 20$

Simplify by adding terms.

Add $- 9 m^{2}$ and $4 m^{2}$ .

$3 m^{3} - 5 m^{2} + 15 m - 12 m + 20$

Subtract $12 m$ from $15 m$ .

$3 m^{3} - 5 m^{2} + 3 m + 20$