Solve left(x-1right)^2left(x+4right)^2

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

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

$$\left(x^{2}-2x+1\right)\left(x^{2}+8x+16\right)$$

Use the distributive property to multiply x^{2}-2x+1 by x^{2}+8x+16 and combine like terms.

$$x^{4}+6x^{3}-24x+x^{2}+16$$

Expand

$$x^{4}+6x^{3}+x^{2}-24x+16$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

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

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

$$\left(x^{2}-2x+1\right)\left(x^{2}+8x+16\right)$$

Use the distributive property to multiply x^{2}-2x+1 by x^{2}+8x+16 and combine like terms.

$$x^{4}+6x^{3}-24x+x^{2}+16$$