# How do you find the product of (3+7v^2)(3-7v^2)?

Jul 22, 2016

$9 - 49 {v}^{4}$

#### Explanation:

This is a binomial $\times$ a binomial.

Each term in the first bracket must be multiplied by each term in the second bracket. This will give $2 \times 2 = 4$ terms.

$\left(3 + 7 {v}^{2}\right) \left(3 - 7 {v}^{2}\right)$

= $9 - 21 {v}^{2} + 21 {v}^{2} - 49 {v}^{4}$

The middle terms are additive inverses, leaving us with..

$9 - 49 {v}^{4}$

We could also have recognised this as the factors of the Difference of two squares (the brackets are the same apart from the signs),

and written down the two squares immediately.