Solve (x-10)^2(x+10)^2

$$( x - 10 ) ^ { 2 } ( x + 10 ) ^ { 2 }$$

Evaluate

$$\left(x^{2}-100\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-10\right)^{2}.

$$\left(x^{2}-20x+100\right)\left(x+10\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+10\right)^{2}.

$$\left(x^{2}-20x+100\right)\left(x^{2}+20x+100\right)$$

Use the distributive property to multiply x^{2}-20x+100 by x^{2}+20x+100 and combine like terms.

$$x^{4}-200x^{2}+10000$$

Expand

$$x^{4}-200x^{2}+10000$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-10\right)^{2}.

$$\left(x^{2}-20x+100\right)\left(x+10\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+10\right)^{2}.

$$\left(x^{2}-20x+100\right)\left(x^{2}+20x+100\right)$$

Use the distributive property to multiply x^{2}-20x+100 by x^{2}+20x+100 and combine like terms.

$$x^{4}-200x^{2}+10000$$