How do you simplify (7+ 2v ) ( 7- 2v )?

Oct 24, 2016

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

Explanation:

$\left(7 + 2 v\right) \left(7 - 2 v\right)$
is of the form $\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2}$

Here , $a = 7$
$b = 2 v$
$\therefore \left(7 + 2 v\right) \left(7 - 2 v\right) = 49 - 4 {v}^{2}$

Oct 24, 2016

$49 - 4 {v}^{2}$

Explanation:

If you do not recognise the expression as the difference of squares as explained by Sibi, you will have to remove the brackets by multiplying out (sometimes called the FOIL rule).

IT does not matter which method you use, but it saves a lot of time if you recoznise the short cut.

$\left(7 + 2 v\right) \left(7 - 2 v\right)$

=$7 \left(7 - 2 v\right) + 2 v \left(7 - 2 v\right)$

=$49 \textcolor{red}{- 14 v + 14 v} - 4 {v}^{2} \text{ } \leftarrow$ notice the additive inverses.

=$49 - 4 {v}^{2} \text{ } \leftarrow$ Difference of squares

If the signs in the brackets are different, the two middle terms will always cancel out.