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

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

Step 1

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

$k^{2} k^{2} + k^{2} \cdot 2 - 5 k \cdot k^{2} - 5 k \cdot 2 - 2 k^{2} - 2 \cdot 2$

Step 2

Simplify terms.

Combine the opposite terms in $k^{2} k^{2} + k^{2} \cdot 2 - 5 k \cdot k^{2} - 5 k \cdot 2 - 2 k^{2} - 2 \cdot 2$ .

Reorder the factors in the terms $k^{2} \cdot 2$ and $- 2 k^{2}$ .

$k^{2} k^{2} + 2 k^{2} - 5 k \cdot k^{2} - 5 k \cdot 2 - 2 k^{2} - 2 \cdot 2$

Subtract $2 k^{2}$ from $2 k^{2}$ .

$k^{2} k^{2} - 5 k \cdot k^{2} - 5 k \cdot 2 + 0 - 2 \cdot 2$

Add $k^{2} k^{2} - 5 k \cdot k^{2} - 5 k \cdot 2$ and $0$ .

$k^{2} k^{2} - 5 k \cdot k^{2} - 5 k \cdot 2 - 2 \cdot 2$

Simplify each term.

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

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

$k^{2 + 2} - 5 k \cdot k^{2} - 5 k \cdot 2 - 2 \cdot 2$

Add $2$ and $2$ .

$k^{4} - 5 k \cdot k^{2} - 5 k \cdot 2 - 2 \cdot 2$

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

Move $k^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $- 5$ .

$k^{4} - 5 k^{3} - 10 k - 2 \cdot 2$

Multiply $- 2$ by $2$ .

$k^{4} - 5 k^{3} - 10 k - 4$