Solve 4a^2-(a-b)^2=

$$4 a ^ { 2 } - ( a - b ) ^ { 2 } =$$

Evaluate

$$\left(3a-b\right)\left(a+b\right)$$

Solution Steps

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

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

To find the opposite of a^{2}-2ab+b^{2}, find the opposite of each term.

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

Combine 4a^{2} and -a^{2} to get 3a^{2}.

$$3a^{2}+2ab-b^{2}$$

Expand

$$3a^{2}+2ab-b^{2}$$

Solution Steps

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

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

To find the opposite of a^{2}-2ab+b^{2}, find the opposite of each term.

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

Combine 4a^{2} and -a^{2} to get 3a^{2}.

$$3a^{2}+2ab-b^{2}$$