Question

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

Answer 1

B. Can I have a medal or Fan

Answer 2

That's not what its looking for.. >.>

Answer 3

Here's an example:

12: 12 = 2*6 = (4-2)(4+2)

Answer 4

the difference of squares is \(4^2-2^2 = 16-4 = 12\)

Answer 5

Make a table of squares:
\[\begin{array}{cc}
x & x^2\\\hline\\
1 & 1 \\
2 & 4 \\
3 & 9 \\
4 & 16 \\
5 & 25 \\
6 & 36 \\
7 & 49 \\
8 & 64 \\
9 & 81 \\
10 & 100 \\
\end{array}\]

Now look down the \(x^2\) column for pairs of numbers that you could subtract to get your number you are trying to factor. For mine, the pair was 16 and 4.

Answer 6

I didn't make the table quite long enough to do one of the problems, but I hope you can figure out how to extend it :-)

Answer 7

so all im doing is squaring them? like 45^2 = 2025?

Answer 8

Im lost please help.. ))): @whpalmer4

Answer 9

@mathmale can you help me on this problem please?

Answer 10

Look at my example. 12 was the number we wanted to factor by difference of squares. Take 12, and successively add it to each number on the right column. After you do, scan down the column and see if you find the sum. If you do, then you've found a pair of factors, namely the values in the left column.

For 12, first I tried 12+1 = 13, but 13 does not appear in the table.
Next, I tried 12+4 = 16. 16 does appear in the table. The left column for the rows containing 4 and 16 contains 2 and 4 respectively, so those were the two numbers, which when squared and the difference taken, gave us 12. \[4^2 - 2^2 = 16-4 = 12\]

Does that make sense now?

Answer 11

That means that our factors were \[(4+2)(4-2) = (6)(2)\]

Answer 12

Here's another example: 9

9+1 = 10, not in the table
9+4 = 13, not in the table
9+9 = 18, not in the table
9+16 = 25, in the table
16 = 4^2
25 =5^2
so 5,4 are our numbers to be squared
\[5^2-4^2 = 25-16 = 9\]\[(5+4)(5-4) = (9)(1)\]so our factors are 9 and 1

Answer 13

Im getting a hold of it hang on let me try the first one and you correct me okay?

Answer 14

It's kind of a weird, roundabout way of factoring a number, and I'm not sure why you would ever do it this way, other than as an exercise in working with the difference of squares.

Sure, give it a shot — I'll get a notification when you post something and I'll come back.

Answer 15

okay so
45+4= 49 which is in the table.

Answer 16

4= 2^2
49= 7^2
7^2-2^2=49-4=45
(7-2) (7+2)=(5)(9) correct?

Answer 17

You got it!

Answer 18

5*9 = 45, just as a check :-)

Answer 19

For bonus points, there's another possible solution for 45, can you spot it?

Answer 20

Oh boy.. you tell my teacher about these bonus points if I get this right haha!

Answer 21

45+19=64?

Answer 22

uh, where do you see 19 in the table?

Answer 23

Wait I have a question about the actual problem. for 112 I did 112+9=121 (I added on to the table) the I did
9=3^3
121=???

Answer 24

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

Answer 25

the bonus points would have been to see that 45 + 36 = 81, so \[(9-6)(9+6) = 3*15 = 45\]