Find the product.

Question

(2v + 5) (2v - 5)=?

Answer 1

Greetings Jamal,

"First, last, inner, outer" is the way I remember solving this type of equation.

(2v + 5) (2v -5) = ?

1. To begin, there is no sign between the parentheses, so you are going to use multiplication to arrive at your solution.
2. First = the first figure in each parenthesis. So that's 2v x 2v = 4v "squared". (Sorry, my computer doesn't type exponents.)
3. Last = the last figure in each parenthesis. So that's (+5) x (-5) = -25.
4. Inner = the 2 figures that are in the most internal place in the pair of parentheses. So that's (+5) in the first parenthesis times (2v) in the second parenthesis. Notice that 2v is in both parentheses.
    Now you've got 2v + 5.
5. Outer = the 2 figures in the most external position in the pair of parentheses. That is 2v in the first parenthesis and  -5 in the second parenthesis. So now you've got 2v - 5.
   Alright?
6. Let's put all of the figures together now:
   (2v + 5) times (2v - 5) =

first: 2v x 2v = 4v squared

last: (+5) (-5 )= -25

inner: +5 x 2v = 10v

outer: -5 x 2v = -10v

It will look like this: (4v)squared - 10v + 10v -25 =

                             (4v)squared - 25 (Remember that -10v +10v = 0)

I hope this helps.

Dianne from Boston MA