(2x+8)(2x-8)

Question

how do you answer this problem?

Answer 1

The product of 2 binomials is also referred to as "FOIL" or double distribution.

Each term in the first factor must be multiplied by each term in the second factor.  These terms are added.

 

So, the 2x needs to be multiplied by (2x-8) and the +8 needs to be also multiplied by (2x-8).

 

2x(2x-8) + 8(2x-8) - hence 2 sets of distribution.  Following through you get:

4x²-16x+16x-64 which can be simplified by combining like terms in the center (these add to 0 or "drop out")

4x²-64. 

 

This is a special product since the middle terms reduced to zero - sometimes called DOTS or Difference of Two (perfect) Squares.  Notice how the two factors of the original problem were almost the same except the 2nd terms were opposites of each other.  These two factors are also known as "conjugates".

Answer 2

These are the factors of a perfect square.  When you see factors such as these you can either remember that they are always going to be the square of the first term (2X) and the square of the second term (8).  Since we see that there is a negative sign in one of the factors we know that the second term will be negative.  Hence, the answer is 4x² - 64.  

 

Another way to look at the solution is by

First multiplying the each term (2x*2x) + 2x*(-8) + 8*2x + 8*(-8)

Solve the multiplications 4x²-16x + 16x -64

add the common terms (-16x+16x)=0

and your solution is again 4x² - 64

 

 

Hope that helps!

Answer 3

you can use the rule

(a-b)(a+b) = a^2 - b^2

 

so for your question

(2x+8)(2x-8) = (2x)^2 - 8^2 = 4x^2 - 64