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

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

Expand

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

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Evaluate

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

Solution Steps

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

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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