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

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

Evaluate

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

Solution Steps

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

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

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

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

Combine a^{2} and a^{2} to get 2a^{2}.

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

Combine 2ab and -2ab to get 0.

$$2a^{2}+b^{2}+b^{2}$$

Combine b^{2} and b^{2} to get 2b^{2}.

$$2a^{2}+2b^{2}$$

Expand

$$2a^{2}+2b^{2}$$

Solution Steps

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

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

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

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

Combine a^{2} and a^{2} to get 2a^{2}.

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

Combine 2ab and -2ab to get 0.

$$2a^{2}+b^{2}+b^{2}$$

Combine b^{2} and b^{2} to get 2b^{2}.

$$2a^{2}+2b^{2}$$