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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply b by 2a+b.

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

Combine -2ab and 2ba to get 0.

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

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

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

Expand

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

Solution Steps

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

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

Use the distributive property to multiply b by 2a+b.

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

Combine -2ab and 2ba to get 0.

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

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

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