## sexy1993 Group Title Find a pair of factors for each number by using the difference of two squares. a. 45 b. 77 c. 112 2 years ago 2 years ago

1. KingGeorge Group Title

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 Group Title

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

3. sexy1993 Group Title

trying to figure it out

4. KingGeorge Group Title

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 Group Title

no sorry

6. KingGeorge Group Title

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 Group Title

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 Group Title

i do not understand how u did this

9. KingGeorge Group Title

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

10. deaunte23 Group Title

c. 8x14