Solve -2(x-3)^2(x^2-1)?

$$- 2 ( x - 3 ) ^ { 2 } ( x ^ { 2 } - 1 ) ?$$

Evaluate

$$-2\left(x-3\right)^{2}\left(x^{2}-1\right)$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$-2\left(x^{2}-6x+9\right)\left(x^{2}-1\right)$$

Use the distributive property to multiply -2 by x^{2}-6x+9.

$$\left(-2x^{2}+12x-18\right)\left(x^{2}-1\right)$$

Use the distributive property to multiply -2x^{2}+12x-18 by x^{2}-1 and combine like terms.

$$-2x^{4}-16x^{2}+12x^{3}-12x+18$$

Expand

$$18-12x-16x^{2}+12x^{3}-2x^{4}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$-2\left(x^{2}-6x+9\right)\left(x^{2}-1\right)$$

Use the distributive property to multiply -2 by x^{2}-6x+9.

$$\left(-2x^{2}+12x-18\right)\left(x^{2}-1\right)$$

Use the distributive property to multiply -2x^{2}+12x-18 by x^{2}-1 and combine like terms.

$$-2x^{4}-16x^{2}+12x^{3}-12x+18$$