Solve x^3(x^4-1)^2

$$x ^ { 3 } ( x ^ { 4 } - 1 ) ^ { 2 }$$

Expand

$$x^{11}-2x^{7}+x^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{4}-1\right)^{2}.

$$x^{3}\left(\left(x^{4}\right)^{2}-2x^{4}+1\right)$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{3}\left(x^{8}-2x^{4}+1\right)$$

Use the distributive property to multiply x^{3} by x^{8}-2x^{4}+1.

$$x^{11}-2x^{7}+x^{3}$$

Evaluate

$$x^{3}\left(x^{4}-1\right)^{2}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x^{4}-1\right)^{2}.

$$x^{3}\left(\left(x^{4}\right)^{2}-2x^{4}+1\right)$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{3}\left(x^{8}-2x^{4}+1\right)$$

Use the distributive property to multiply x^{3} by x^{8}-2x^{4}+1.

$$x^{11}-2x^{7}+x^{3}$$