SOLUTION: Says to factor by grouping? 40a^4-120a^2+90

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Question 191276: Says to factor by grouping?
40a^4-120a^2+90

Found 3 solutions by Edwin McCravy, kara!, Mathtut:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Says to factor by grouping?
40a^4-120a^2+90

40a%5E4-120a%5E2%2B90

First factor out 10

10%284a%5E4-12a%5E2%2B9%29

In the parentheses, multiply the first coefficient 4
by the last coefficient 9, getting 36.  Write down
all pairs of integer factors whose product is 36.
They are

1*36
2*18
3*12
4*9
6*6

Since the last sign in the parentheses is +, we
add those:

1+36 = 37
2+18 = 20
3+12 = 15
 4+9 = 13 
 6+6 = 12

Since the middle coefficient of %284a%5E4-12a%5E2%2B9%29
is 12, and since 12 = 6+6 we write -12a^2 as -6a^2-6a^2

10%284a%5E4-12a%5E2%2B9%29

10%284a%5E4-6a%5E2-6a%5E2%2B9%29

Factor the first two terms in the parentheses by factoring 
out 2a%5E2

10%282a%5E2%282a%5E2-3%29-6a%5E2%2B9%29
 
Factor the last two terms in the parentheses by factoring 
out -3

10%282a%5E2%282a%5E2-3%29-3%282a%5E2-3%29%29

Inside the outer parentheses take out 
the inner parentheses %282a%5E2-3%29

10%282a%5E2-3%29%282a%5E2-3%29

Notice the parenthesis can be written once as squared:

10%282a%5E2-3%29%5E2

Edwin

Answer by kara!(17) About Me  (Show Source):
You can put this solution on YOUR website!
10*(4*a^4-12*a^2+9)
10*((2a^2)^2-2*2*3a^2+3^2)
10(2a^2-3)^2

Answer by Mathtut(3670) About Me  (Show Source):