Factoring the difference of squares math question??

Question

I wasn't at school for math for a couple days and I really need to know this since I have a test on monday...

The question says

"Remove the common factors, then factor using a difference of squares"


1. 8a(squared) -50


2. 50y(squared) -72

Could someone please help me with these.
Show me the answer step through step and try and make it as simple as possible so I'll be ready for my test.

Thanks

The answer key says that the answers are a(2a-5)(2a+5) and 2(5y-6)(5y+6) how do I get that??

Answer 1

1. 8a^2 - 50
remove GCF, the biggest number that 8 and 50 can both be divided by is 2 so you divide 8 and 50 both by 2.

4a^2 - 25

Now you factor by reverse foiling, meaning you set up something like this

(2a +/- X)(2a +/- Y) and you have to figure out the signs and the X and Y by guess and check, the 25 is being subtracted so you know that you will have the following

(2a+X)(2a-X) this will result in a 4a^2 - XY and you know XY must equal 25 so you think of all the whole numbers that can br multiplied together to get 25...5 and 5 and you plug in

(2a-5)(2a+5) this when foiled will give you 4a^2 - 25 but to get your original equation you were ask to factor you must place the GCF in front of the factors:

2(2a-5)(2a+5) and this wil give you 8a^2 - 50

2. 50y^2 - 72
GCF: 2 25y^2 - 36

(5y-X)(5y+Y) XY=36
(5y-6)(5y+6)= 25y^2 - 36
2(5y-6)(5y+6)= 50y^2 - 72

Answer 2

To take out the common factors, just divide by whatever number they have in common.

8 a^2 - 50 Divide the 8 and the 50 by 2; they have 2 in common.
4 a^2 - 25 This is the difference of two squares which just means it's one square minus another square.

To factor the difference of two squares, the first factor will be the square root of the first part PLUS the square root of the second part. (2a + 5) for this problem. The second factor will be the same thing only with a MINUS sign. (2a - 5) for this problem. It doesn't matter if you put the PLUS or the MINUS first, just have one of each.

8 a^2 - 50
2(4 a^2 - 25)
2 (2a + 5)(2a - 5)

Do the second one in the same way.

50 y^2 - 72 Factor out a 2.
2 (25 y^2 - 36) Now you have the difference of two squares.
2 (5y + 6)(5y -6)

Answer 3

1) 8a square -50
2(4a square -25)
2(2a-5) ( 2a+ 5) that is the answer, when you do the FOIL, you will get 8a square -50.

2) 50y square -72
2(25y square-36)
2(5y+6) ( 5y-6) the sign in the middle of both column is always different. IT doesn't matter which one(+ or -) goes first.

do you get it? I hope so, i am sorry I don't know how to explain.

Answer 4

8a^2 - 50

take out common factor - find the highest common number that goes into both of them. We'll say it's 2 because 2 goes into 8 four times and 2 goes into 50 twenty-five times.

2 [4a^2 - 25]

then factorise