factoring 2x^2-7xy+3y^2+9x-7y+4, a^2-4b^2-3c^2+8bc-2ac,  TOPIC_SOLVED

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factoring 2x^2-7xy+3y^2+9x-7y+4, a^2-4b^2-3c^2+8bc-2ac,

Postby thomasphilips on Sat Mar 09, 2013 4:40 pm

how to factor the following

2x^2-7xy+3y^2+9x-7y+4

a^2-4b^2-3c^2+8bc-2ac

a^2+5ab+5a-6b^2-12b-6
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Re: factoring 2x^2-7xy+3y^2+9x-7y+4, a^2-4b^2-3c^2+8bc-2ac,  TOPIC_SOLVED

Postby anonmeans on Sun Mar 10, 2013 11:15 pm

thomasphilips wrote:how to factor the following

2x^2-7xy+3y^2+9x-7y+4

You can do three terms like a regular trinomial:

2x^2 - 7xy + 3y^2 = 2x^2 - 6xy - 1xy + 3y^2 = (2x - y)(x - 3y)

To finish the factoring, you have to find some way of making the rest fit with this first part. So do like this:

(2x - y + A)(x - 3y + B) = (2x - y)(x - 3y) + (2x - y)(B) + A(x - 3y) + AB
= (2x^2 - 7xy + 3y^2) + 2Bx - By + Ax - 3Ay + AB
= (2x^2 - 7xy + 3y^2) + (2B + A)x + (-B - 3A)y + AB

Then A + 2B = 9, -3A - B = -7, and AB = 4. Solve the system to find the factorization:

A = 9 - 2B

-3(9 - 2B) - B = -7
-27 + 6B - B = -7
5B = 20
B = 4

A = 9 - 2(4) = 9 - 8 = 1

check: AB = 1*4 = 4

thomasphilips wrote:a^2-4b^2-3c^2+8bc-2ac

a^2+5ab+5a-6b^2-12b-6

Try doing these the same way. Plz write back if you get stuck. Thnx.
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