Solve (x-1)^3(x+1)^3

$$( x - 1 ) ^ { 3 } ( x + 1 ) ^ { 3 }$$

Evaluate

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

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

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

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.

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

Use the distributive property to multiply x^{3}-3x^{2}+3x-1 by x^{3}+3x^{2}+3x+1 and combine like terms.

$$x^{6}-3x^{4}+3x^{2}-1$$

Expand

$$x^{6}-3x^{4}+3x^{2}-1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

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

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+1\right)^{3}.

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

Use the distributive property to multiply x^{3}-3x^{2}+3x-1 by x^{3}+3x^{2}+3x+1 and combine like terms.

$$x^{6}-3x^{4}+3x^{2}-1$$