Solve (x+1)^2-(x-1)^2<4

$$( x + 1 ) ^ { 2 } - ( x - 1 ) ^ { 2 } < 4$$

Solve for x

$$x<1$$

Solution Steps

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

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

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

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

To find the opposite of x^{2}-2x+1, find the opposite of each term.

$$x^{2}+2x+1-x^{2}+2x-1<4$$

Combine x^{2} and -x^{2} to get 0.

$$2x+1+2x-1<4$$

Combine 2x and 2x to get 4x.

$$4x+1-1<4$$

Subtract 1 from 1 to get 0.

$$4x<4$$

Divide both sides by 4. Since 4 is positive, the inequality direction remains the same.

$$x<\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$x<1$$