Question

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

Answer 1

a. 49 -4 = 7² - 2² = (7+2)(7-2) ??? am i on the right track with these???

Answer 2

b. 81 -4 = 9^2 - 2^2 = (9+2)(9-2)
c. 121 -9 = 11^2 - 3^ = (11+3)(11-3)

Answer 3

Let's start with a. Using difference of two squares, note that 45=49−4=72−22This last expression can be factored easily as
72−22=(7−2)⋅(7+2)
Hence, your factorization is 9⋅5

Answer 4

For b, we want to write
77=81−4=92−22


There's an easy way to factorize a difference of two squares. If you have a differnece of two squares
a2−b2
then this factors into
a2−b2=(a−b)⋅(a+b)
Does this help?


So you have an equation of the form
a2−b2
where a=9 and b=2. Thus,
a2−b2=(a−b)⋅(a+b)
can be replaced by
92−22=(9−2)⋅(9+2)
Which then simplifies to
7⋅11

Let's move on to c. We want to factor 112. Notice that
112=121−9=112−32
Using the same principles as above,

Answer 5

c. 80, 32 ???

Answer 6

c. 8, 14 ????

Answer 7

i'm so confused!

Answer 8

Wait , let me break this down to you.
a. 45 = (7-2)(7+2)
b. 77 = (9-2)(9+2)
c. 112 = (11-3)(11+3)

so therefore, if you go with c , it may likely be your answer , lol im kinda confused here as well