Solve 7left(a+2bright)^2-21left(a+2bright)

$$7 { \left(a+2b \right) }^{ 2 } -21 \left( a+2b \right)$$

Evaluate

$$7\left(a+2b\right)\left(a+2b-3\right)$$

Solution Steps

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

$$7\left(a^{2}+4ab+4b^{2}\right)-21\left(a+2b\right)$$

Use the distributive property to multiply 7 by a^{2}+4ab+4b^{2}.

$$7a^{2}+28ab+28b^{2}-21\left(a+2b\right)$$

Use the distributive property to multiply -21 by a+2b.

$$7a^{2}+28ab+28b^{2}-21a-42b$$

Expand

$$7a^{2}+28ab-21a+28b^{2}-42b$$

Solution Steps

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

$$7\left(a^{2}+4ab+4b^{2}\right)-21\left(a+2b\right)$$

Use the distributive property to multiply 7 by a^{2}+4ab+4b^{2}.

$$7a^{2}+28ab+28b^{2}-21\left(a+2b\right)$$

Use the distributive property to multiply -21 by a+2b.

$$7a^{2}+28ab+28b^{2}-21a-42b$$