How do you multiply (4u+7v)^2?

Aug 19, 2016

${\left(4 u + 7 v\right)}^{2} = 16 {u}^{2} + 56 u v + 49 {v}^{2}$

Explanation:

${\left(4 u + 7 v\right)}^{2}$

= $\left(4 u + 7 v\right) \left(4 u + 7 v\right)$

= $4 u \left(4 u + 7 v\right) + 7 v \left(4 u + 7 v\right)$

= 4u×4u+4u×7v+7v×4u+7v×7v

= $16 {u}^{2} + 28 u v + 28 u v + 49 {v}^{2}$

= $16 {u}^{2} + 56 u v + 49 {v}^{2}$