SOLUTION: Could you please help me to factor this to the lowest and simplest form. thank you so much. 12x^2y^2 + 10xy^2 – 42y^2

Algebra ->  Expressions -> SOLUTION: Could you please help me to factor this to the lowest and simplest form. thank you so much. 12x^2y^2 + 10xy^2 – 42y^2       Log On


   

Question 103829: Could you please help me to factor this to the lowest and simplest form. thank you so much.
12x^2y^2 + 10xy^2 – 42y^2
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
12x%5E2y%5E2+%2B+10xy%5E2 - 42y%5E2%29+
2y%5E2 is a common factor of all three terms, so pull it out
2y%5E2%286x%5E2+%2B+5x+-+21%29+
now we can factor 6x%5E2+%2B+5x+-+21+
replace 5xwith -9x+%2B+14x
now we have 6x%5E2+-+9x+%2B+14x+-+21+ group the first two terms together and the last two terms
now we have %286x%5E2+-+9x%29+%2B+%2814x+-+21%29+
3x is a common factor of both terms in the first group, and 7 is a common factor in the second group; so, pull it out and you will have
3x%282x+-+3%29+%2B+7%282x+-+3%29+
2x+-+3 is a common factor of both terms; so, factor it out and you will have
%282x+-+3%29%283x+%2B+7%29

now go back to 2y%5E2%286x%5E2+%2B+5x+-+21%29+ and substitute 6x%5E2+%2B+5x+-+21+
with %282x+-+3%29%283x+%2B+7%29

and you will have:
2y%5E2%282x+-+3%29%283x+%2B+7%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
factor this to the lowest and simplest form. thank you so much.
12x^2y^2 + 10xy^2 – 42y^2
--------------------
= 2y^2(6x^2 + 5x - 21)

= 2y^2(2x-3)3x+7)
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Cheers,
Stan H.