Simplify (7k-3)(k^2-2k+7)

$(7 k - 3) (k^{2} - 2 k + 7)$

Step 1

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

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

Step 2

Simplify terms.

Simplify each term.

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

Move $k^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $k$ .

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

Multiply $k$ by $k$ .

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

Multiply $7$ by $- 2$ .

$7 k^{3} - 14 k^{2} + 7 k \cdot 7 - 3 k^{2} - 3 (- 2 k) - 3 \cdot 7$

Multiply $7$ by $7$ .

$7 k^{3} - 14 k^{2} + 49 k - 3 k^{2} - 3 (- 2 k) - 3 \cdot 7$

Multiply $- 2$ by $- 3$ .

$7 k^{3} - 14 k^{2} + 49 k - 3 k^{2} + 6 k - 3 \cdot 7$

Multiply $- 3$ by $7$ .

$7 k^{3} - 14 k^{2} + 49 k - 3 k^{2} + 6 k - 21$

Simplify by adding terms.

Subtract $3 k^{2}$ from $- 14 k^{2}$ .

$7 k^{3} - 17 k^{2} + 49 k + 6 k - 21$

Add $49 k$ and $6 k$ .

$7 k^{3} - 17 k^{2} + 55 k - 21$