Solve (x^2-4)(x^2+3x)(x-2)

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

Evaluate

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

Solution Steps

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

$$\left(x^{4}+3x^{3}-4x^{2}-12x\right)\left(x-2\right)$$

Use the distributive property to multiply x^{4}+3x^{3}-4x^{2}-12x by x-2 and combine like terms.

$$x^{5}+x^{4}-10x^{3}-4x^{2}+24x$$

Expand

$$x^{5}+x^{4}-10x^{3}-4x^{2}+24x$$

Solution Steps

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

$$\left(x^{4}+3x^{3}-4x^{2}-12x\right)\left(x-2\right)$$

Use the distributive property to multiply x^{4}+3x^{3}-4x^{2}-12x by x-2 and combine like terms.

$$x^{5}+x^{4}-10x^{3}-4x^{2}+24x$$