Solve (a+b)^2-(b^2)^2

$$( a + b ) ^ { 2 } - ( b ^ { 2 } ) ^ { 2 }$$

Evaluate

$$-b^{4}+\left(a+b\right)^{2}$$

Solution Steps

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

$$\left(a+b\right)^{2}-b^{4}$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}+2ab+b^{2}-b^{4}$$

Expand

$$a^{2}+2ab-b^{4}+b^{2}$$

Solution Steps

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

$$\left(a+b\right)^{2}-b^{4}$$

Use binomial theorem \left(p+q\right)^{2}=p^{2}+2pq+q^{2} to expand \left(a+b\right)^{2}.

$$a^{2}+2ab+b^{2}-b^{4}$$