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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $k^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $3$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $k$ by $k$ by adding the exponents.

Move $k$ .

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

Multiply $k$ by $k$ .

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

Multiply $3$ by $- 5$ .

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

Multiply $- 3$ by $3$ .

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

Multiply $3$ by $4$ .

$9 k^{3} - 15 k^{2} - 9 k + 12 k^{2} + 4 (- 5 k) + 4 \cdot - 3$

Multiply $- 5$ by $4$ .

$9 k^{3} - 15 k^{2} - 9 k + 12 k^{2} - 20 k + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

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

Simplify by adding terms.

Add $- 15 k^{2}$ and $12 k^{2}$ .

$9 k^{3} - 3 k^{2} - 9 k - 20 k - 12$

Subtract $20 k$ from $- 9 k$ .

$9 k^{3} - 3 k^{2} - 29 k - 12$