Solve left(2a+bright)^2-6(2a+b)+9

$${ \left(2a+b \right) }^{ 2 } -6(2a+b)+9$$

Evaluate

$$\left(2a+b-3\right)^{2}$$

Solution Steps

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

$$4a^{2}+4ab+b^{2}-6\left(2a+b\right)+9$$

Use the distributive property to multiply -6 by 2a+b.

$$4a^{2}+4ab+b^{2}-12a-6b+9$$

Expand

$$4a^{2}+4ab-12a+b^{2}-6b+9$$

Solution Steps

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

$$4a^{2}+4ab+b^{2}-6\left(2a+b\right)+9$$

Use the distributive property to multiply -6 by 2a+b.

$$4a^{2}+4ab+b^{2}-12a-6b+9$$