Solve (x-1)^2(x+9)^2

$$( x - 1 ) ^ { 2 } ( x + 9 ) ^ { 2 }$$

Evaluate

$$\left(\left(x-1\right)\left(x+9\right)\right)^{2}$$

Solution Steps

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

$$\left(x^{2}-2x+1\right)\left(x+9\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+9\right)^{2}.

$$\left(x^{2}-2x+1\right)\left(x^{2}+18x+81\right)$$

Use the distributive property to multiply x^{2}-2x+1 by x^{2}+18x+81 and combine like terms.

$$x^{4}+16x^{3}+46x^{2}-144x+81$$

Expand

$$x^{4}+16x^{3}+46x^{2}-144x+81$$

Solution Steps

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

$$\left(x^{2}-2x+1\right)\left(x+9\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+9\right)^{2}.

$$\left(x^{2}-2x+1\right)\left(x^{2}+18x+81\right)$$

Use the distributive property to multiply x^{2}-2x+1 by x^{2}+18x+81 and combine like terms.

$$x^{4}+16x^{3}+46x^{2}-144x+81$$