How do you find the product of (6v+3)(6v-3)?

Jun 29, 2016

$\left(6 v + 3\right) \left(6 v - 3\right) = 36 {v}^{2} - 9$

Explanation:

We can use the identity $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

Here we have $\left(6 v + 3\right) \left(6 v - 3\right)$

= ${\left(6 v\right)}^{2} - {3}^{2}$

= $36 {v}^{2} - 9$

Even if one intends to multiply

$\left(6 v + 3\right) \left(6 v - 3\right)$

= $6 v \left(6 v - 3\right) + 3 \left(6 v - 3\right)$

= ${\left(6 v\right)}^{2} - 18 v + 18 v - {3}^{2}$

= $36 {v}^{2} - 9$