SOLUTION: (Factorise) Find the difference of two squares: 8x^2-2y^2 Please show all working

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Question 1026660: (Factorise) Find the difference of two squares:
8x^2-2y^2
Please show all working
Found 3 solutions by Edwin McCravy, Theo, MathTherapy:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
8x%5E2-2y%5E2

First we can take out a common factor of 2:

2%284x%5E2-y%5E2%29

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We learn the principle of factorising the 
difference of two squares. Here 
is why it works:

A²-B² = (A-B)(A+B)

Proof: (A-B)(A+B) = A²+AB-AB-B² = A²-B²

So we memorise:

A²-B² is factorized as (A-B)(A+B)

--------------------------------------

Now back to this:

2%284x%5E2-y%5E2%29

Since 4=2², we can rewrite that as

2%282%5E2x%5E2-y%5E2%29

and again as

2%28%282x%29%5E2-y%5E2%29

Since we have memorized that

A²-B² is factorised as (A-B)(A+B)

We can substitute 2x for A and y for B and get that

2%28%282x%29%5E2-y%5E2%29%29 is factorised as 2%282x-y%29%282x%2By%29

Edwin

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see the worksheet below.

look below the worksheet for further comments.

$$$.

these follow the form of (a^2 - b^2) = (a-b) * (a+b)

in this problem, a^2 = 8x^2 and b^2 = 2y^2.

to find a, take the square root of 8x^2 to get sqrt(8) * x.

to find b, take the square root of 2y^2 to get sqrt(2) * y.

the rest follows as shown in the worksheet.






Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

(Factorise) Find the difference of two squares:
8x^2-2y^2
Please show all working
8x%5E2+-+2y%5E2

2%284x%5E2+-+y%5E2%29 ---------- Factoring out GCF, 2

highlight_green%282%282x+-+y%29%282x+%2B+y%29%29 ----- Factorizing DOTS: 4x%5E2+-+y%5E2