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

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

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $k^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $3$ by $2$ .

$6 k^{3} + 3 k (- 5 k) + 3 k \cdot - 3 + 5 (2 k^{2}) + 5 (- 5 k) + 5 \cdot - 3$

Rewrite using the commutative property of multiplication.

$6 k^{3} + 3 \cdot - 5 k \cdot k + 3 k \cdot - 3 + 5 (2 k^{2}) + 5 (- 5 k) + 5 \cdot - 3$

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

Move $k$ .

$6 k^{3} + 3 \cdot - 5 (k \cdot k) + 3 k \cdot - 3 + 5 (2 k^{2}) + 5 (- 5 k) + 5 \cdot - 3$

Multiply $k$ by $k$ .

$6 k^{3} + 3 \cdot - 5 k^{2} + 3 k \cdot - 3 + 5 (2 k^{2}) + 5 (- 5 k) + 5 \cdot - 3$

Multiply $3$ by $- 5$ .

$6 k^{3} - 15 k^{2} + 3 k \cdot - 3 + 5 (2 k^{2}) + 5 (- 5 k) + 5 \cdot - 3$

Multiply $- 3$ by $3$ .

$6 k^{3} - 15 k^{2} - 9 k + 5 (2 k^{2}) + 5 (- 5 k) + 5 \cdot - 3$

Multiply $2$ by $5$ .

$6 k^{3} - 15 k^{2} - 9 k + 10 k^{2} + 5 (- 5 k) + 5 \cdot - 3$

Multiply $- 5$ by $5$ .

$6 k^{3} - 15 k^{2} - 9 k + 10 k^{2} - 25 k + 5 \cdot - 3$

Multiply $5$ by $- 3$ .

$6 k^{3} - 15 k^{2} - 9 k + 10 k^{2} - 25 k - 15$

Simplify by adding terms.

Add $- 15 k^{2}$ and $10 k^{2}$ .

$6 k^{3} - 5 k^{2} - 9 k - 25 k - 15$

Subtract $25 k$ from $- 9 k$ .

$6 k^{3} - 5 k^{2} - 34 k - 15$