## sexy1993 3 years ago Find a pair of factors for each number by using the difference of two squares. a. 45 b. 77 c. 112

1. KingGeorge

Let's start with a. Using difference of two squares, note that $$45=49-4=7^2-2^2$$This last expression can be factored easily as $7^2-2^2=(7-2)\cdot(7+2)$Hence, your factorization is $$9\cdot 5$$

2. KingGeorge

For b, we want to write$77=81-4=9^2-2^2$Can you factorize from there?

3. sexy1993

trying to figure it out

4. KingGeorge

There's an easy way to factorize a difference of two squares. If you have a differnece of two squares $a^2-b^2$then this factors into$a^2-b^2=(a-b)\cdot(a+b)$Does this help?

5. sexy1993

no sorry

6. KingGeorge

So you have an equation of the form $a^2-b^2$where $$a=9$$ and $$b=2$$. Thus, $a^2-b^2=(a-b)\cdot(a+b)$can be replaced by $9^2-2^2=(9-2)\cdot(9+2)$Which then simplifies to $7\cdot11$

7. KingGeorge

Let's move on to c. We want to factor 112. Notice that $112=121-9=11^2-3^2$Using the same principles as above, can you try to factor this one?

8. sexy1993

i do not understand how u did this

9. KingGeorge

Sorry, I had to go get dinner. What part of this do you now understand?

10. deaunte23

c. 8x14