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

Question

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

kinggeorge · Answer

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 $9\cdot 5$

kinggeorge · Answer

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

anonymous · Answer

trying to figure it out

kinggeorge · Answer

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?

anonymous · Answer

no sorry

kinggeorge · Answer

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 $$7\cdot11$$

kinggeorge · Answer

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?

anonymous · Answer

i do not understand how u did this

kinggeorge · Answer

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

anonymous · Answer

c. 8x14