Solve left(x-2right)^2left(x+2right)^2left(x+4right)^2

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

Evaluate

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

Solution Steps

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

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

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

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$\left(x^{2}-4x+4\right)\left(x^{2}+4x+4\right)\left(x^{2}+8x+16\right)$$

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

$$\left(x^{4}-8x^{2}+16\right)\left(x^{2}+8x+16\right)$$

Use the distributive property to multiply x^{4}-8x^{2}+16 by x^{2}+8x+16 and combine like terms.

$$x^{6}+8x^{5}+8x^{4}-64x^{3}-112x^{2}+128x+256$$

Expand

$$x^{6}+8x^{5}+8x^{4}-64x^{3}-112x^{2}+128x+256$$

Solution Steps

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

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

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

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$\left(x^{2}-4x+4\right)\left(x^{2}+4x+4\right)\left(x^{2}+8x+16\right)$$

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

$$\left(x^{4}-8x^{2}+16\right)\left(x^{2}+8x+16\right)$$

Use the distributive property to multiply x^{4}-8x^{2}+16 by x^{2}+8x+16 and combine like terms.

$$x^{6}+8x^{5}+8x^{4}-64x^{3}-112x^{2}+128x+256$$