Simplify (-x^2-2x-2)(x^2+x-3)

$(- x^{2} - 2 x - 2) (x^{2} + x - 3)$

Step 1

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

$- x^{2} x^{2} - x^{2} x - x^{2} \cdot - 3 - 2 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

Step 2

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

$- (x^{2} x^{2}) - x^{2} x - x^{2} \cdot - 3 - 2 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

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

$- x^{2 + 2} - x^{2} x - x^{2} \cdot - 3 - 2 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

Add $2$ and $2$ .

$- x^{4} - x^{2} x - x^{2} \cdot - 3 - 2 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

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

Move $x$ .

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

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

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

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

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

$- x^{4} - x^{1 + 2} - x^{2} \cdot - 3 - 2 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

Add $1$ and $2$ .

$- x^{4} - x^{3} - x^{2} \cdot - 3 - 2 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

Multiply $- 3$ by $- 1$ .

$- x^{4} - x^{3} + 3 x^{2} - 2 x \cdot x^{2} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

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

Move $x^{2}$ .

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

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

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

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

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

$- x^{4} - x^{3} + 3 x^{2} - 2 x^{2 + 1} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

Add $2$ and $1$ .

$- x^{4} - x^{3} + 3 x^{2} - 2 x^{3} - 2 x \cdot x - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

$- x^{4} - x^{3} + 3 x^{2} - 2 x^{3} - 2 x^{2} - 2 x \cdot - 3 - 2 x^{2} - 2 x - 2 \cdot - 3$

Multiply $- 3$ by $- 2$ .

$- x^{4} - x^{3} + 3 x^{2} - 2 x^{3} - 2 x^{2} + 6 x - 2 x^{2} - 2 x - 2 \cdot - 3$

Multiply $- 2$ by $- 3$ .

$- x^{4} - x^{3} + 3 x^{2} - 2 x^{3} - 2 x^{2} + 6 x - 2 x^{2} - 2 x + 6$

Simplify by adding terms.

Subtract $2 x^{3}$ from $- x^{3}$ .

$- x^{4} - 3 x^{3} + 3 x^{2} - 2 x^{2} + 6 x - 2 x^{2} - 2 x + 6$

Subtract $2 x^{2}$ from $3 x^{2}$ .

$- x^{4} - 3 x^{3} + x^{2} + 6 x - 2 x^{2} - 2 x + 6$

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

$- x^{4} - 3 x^{3} - x^{2} + 6 x - 2 x + 6$

Subtract $2 x$ from $6 x$ .

$- x^{4} - 3 x^{3} - x^{2} + 4 x + 6$

Simplify (-x^2-2x-2)(x^2+x-3)

Related Questions

Support LCMGCF.com by disabling your adblocker.