Solve left(2a-bright)^2+left(4a-2bright)left(a+bright)+a+b

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

Evaluate

$$8a^{2}-2ab+a-b^{2}+b$$

Solution Steps

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

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

Use the distributive property to multiply 4a-2b by a+b and combine like terms.

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

Combine 4a^{2} and 4a^{2} to get 8a^{2}.

$$8a^{2}-4ab+b^{2}+2ab-2b^{2}+a+b$$

Combine -4ab and 2ab to get -2ab.

$$8a^{2}-2ab+b^{2}-2b^{2}+a+b$$

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

$$8a^{2}-2ab-b^{2}+a+b$$

Expand

$$8a^{2}-2ab+a-b^{2}+b$$

Solution Steps

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

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

Use the distributive property to multiply 4a-2b by a+b and combine like terms.

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

Combine 4a^{2} and 4a^{2} to get 8a^{2}.

$$8a^{2}-4ab+b^{2}+2ab-2b^{2}+a+b$$

Combine -4ab and 2ab to get -2ab.

$$8a^{2}-2ab+b^{2}-2b^{2}+a+b$$

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

$$8a^{2}-2ab-b^{2}+a+b$$