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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply x^{2}-4x+4 by x^{2}-1 and combine like terms.

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

Use the distributive property to multiply x^{4}+3x^{2}-4x^{3}+4x-4 by x+3 and combine like terms.

$$x^{5}-x^{4}-9x^{3}+13x^{2}+8x-12$$

Expand

$$x^{5}-x^{4}-9x^{3}+13x^{2}+8x-12$$

Solution Steps

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

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

Use the distributive property to multiply x^{2}-4x+4 by x^{2}-1 and combine like terms.

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

Use the distributive property to multiply x^{4}+3x^{2}-4x^{3}+4x-4 by x+3 and combine like terms.

$$x^{5}-x^{4}-9x^{3}+13x^{2}+8x-12$$