Solve (j-1)^2(j+1)^2

$$( j - 1 ) ^ { 2 } ( j + 1 ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

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

$$j^{4}-2j^{2}+1$$

Expand

$$j^{4}-2j^{2}+1$$

Solution Steps

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

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

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

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

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

$$j^{4}-2j^{2}+1$$