Solve (x-5)^2(x+5)^2

$$( x - 5 ) ^ { 2 } ( x + 5 ) ^ { 2 }$$

Evaluate

$$\left(x^{2}-25\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$\left(x^{2}-10x+25\right)\left(x+5\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$\left(x^{2}-10x+25\right)\left(x^{2}+10x+25\right)$$

Use the distributive property to multiply x^{2}-10x+25 by x^{2}+10x+25 and combine like terms.

$$x^{4}-50x^{2}+625$$

Expand

$$x^{4}-50x^{2}+625$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-5\right)^{2}.

$$\left(x^{2}-10x+25\right)\left(x+5\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$\left(x^{2}-10x+25\right)\left(x^{2}+10x+25\right)$$

Use the distributive property to multiply x^{2}-10x+25 by x^{2}+10x+25 and combine like terms.

$$x^{4}-50x^{2}+625$$