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

Question

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

jim_thompson5910 · Answer

a)

Notice how 

45 = 9*5

45 = (7+2)*(7-2)

45 = 7^2 - 2^2

45 = 49 - 4

-------------

So going backwards, you can say


45 = 49 - 4

45 = 7^2 - 2^2

45 = (7+2)*(7-2)

45 = 9*5

anonymous · Answer

ok so what do i do next

jim_thompson5910 · Answer

Use this technique to do parts b) and c)

Let me know what you get

anonymous · Answer

hold on i will be right back

jim_thompson5910 · Answer

alright

anonymous · Answer

does it make a difference if you go backwards or not also

jim_thompson5910 · Answer

I'm just showing you how I got the stuff under the "------" line. You don't have to go backwards if you know how to go forwards (if that makes any sense)

anonymous · Answer

oh ok yes it does ok hold on

jim_thompson5910 · Answer

sure thing

anonymous · Answer

could you help

jim_thompson5910 · Answer

where are you stuck?

anonymous · Answer

still on 77... :(

jim_thompson5910 · Answer

that's ok

jim_thompson5910 · Answer

77 = 11*7

77 = (9+2)*(9-2)

77 = 9^2 - 2^2

77 = 81 - 4

------------------

Now go backwards

77 = 81 - 4

77 = 9^2 - 2^2

77 = (9+2)*(9-2)

77 = 11*7

So the idea is that you work out the first part on scratch paper. Then the second part is what you do on your hw

anonymous · Answer

ok i am stuck on the (+) (-) part on 112

anonymous · Answer

on the first part so far i have 112= 8*14

jim_thompson5910 · Answer

so 

112 = 8*14

112 = (11-3)*(11+3)

anonymous · Answer

ok so i got 
112=8*14
112=(11+3)(11-3)
112=11^3- 3^3
112=116-4

jim_thompson5910 · Answer

you square, not cube

jim_thompson5910 · Answer

so your 3rd step should be 112 = 11^2 - 3^2

anonymous · Answer

oh ok soo what do i do next

jim_thompson5910 · Answer

11^2 = 121, 3^2 = 9

so 

112 = 11^2 - 3^2

becomes

112 = 121 - 9

jim_thompson5910 · Answer

Now go backwards: start with 112 = 121 - 9 and work your way up to find the factorization for 112

anonymous · Answer

112=121-9
112=11^2-3^2
112=(11-3)*(11+3)
112=8*14

jim_thompson5910 · Answer

good, you nailed it

anonymous · Answer

ok so what do i put as the answer? the whole things we just worked on

jim_thompson5910 · Answer

what you just wrote is your answer for part c)

jim_thompson5910 · Answer

the other parts are similar (just use different numbers)

anonymous · Answer

so a. is all that with 45 and b is all that with 77 and c. is all that with 112 is the answers?

jim_thompson5910 · Answer

yes pretty much, half is scratch work so you know how to start each one

jim_thompson5910 · Answer

but you might as well include it

anonymous · Answer

alrighty Thanks so much

jim_thompson5910 · Answer

yw