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Factor the polynomial 1x^3-9xy^2+7x^2-63 y^2 into a product of 3 polynomials A*B*C?
I've tried this problem 50 times and I just can't get the right answer! I would really really appreciate if someone could help me figure out how to do it :)
2 Answers
- 9 years ago
You have to use factoring by grouping.
Take the first two terms, and factor out the GCF: x
x^3-9xy^2 = x(x^2-9y^2)
Take the second two terms and factor out the GCF: 7
7x^2-63 y^2= +7(x^2-9 y^2)
The x from the first "group" and the 7 from the second "group" become one product (x+7).
The (x^2-9 y^2) is a second product that is also a difference of squares.
Now you have (x+7)(x^2-9 y^2). A difference of square always factors to (x+a)(x-a)....in this case:
(x+7)(x-3y)(x+3y)
- Anonymous9 years ago
x³-9xy²+7x²-63y² =
(x²-9)(xy²+7) =
x(x-9)(y²+7)
↓↓↓↓↓↓↓↓↓↓↓↓↓↓
x³y²-9xy²+7x²-63
:D
