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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $k^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $k$ .

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

Multiply $k$ by $k$ .

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

Multiply $2$ by $- 4$ .

$4 k^{3} - 8 k^{2} + 2 k \cdot - 3 + 3 (2 k^{2}) + 3 (- 4 k) + 3 \cdot - 3$

Multiply $- 3$ by $2$ .

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

Multiply $2$ by $3$ .

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

Multiply $- 4$ by $3$ .

$4 k^{3} - 8 k^{2} - 6 k + 6 k^{2} - 12 k + 3 \cdot - 3$

Multiply $3$ by $- 3$ .

$4 k^{3} - 8 k^{2} - 6 k + 6 k^{2} - 12 k - 9$

Simplify by adding terms.

Add $- 8 k^{2}$ and $6 k^{2}$ .

$4 k^{3} - 2 k^{2} - 6 k - 12 k - 9$

Subtract $12 k$ from $- 6 k$ .

$4 k^{3} - 2 k^{2} - 18 k - 9$