How do you factor #12x^7y^9+6x^4y^7-10x^3y^5#?

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Answer 1 · 2016-11-28T22:04:14

#2x^3y^5(6x^4y^4 + 3xy^2 - 5)#

You need to pull the highest common value out of each variable and constant in the terms:

For the constants 12, 6 and 10 the highest common value is 2

For #x# the highest common value is #x^3#

For #y# the highest common value is #y^5#

So, we can rewrite this problem, using the rules for exponents as:

#2x^3y^5(6x^(7-3)y^(9-5)+ 3x^(4-3)y^(7-5) - 5x^(3-3)y^(5-5)) =>#

#2x^3y^5(6x^4y^4 + 3x^1y^2 - 5x^0y^0) =>#

#2x^3y^5(6x^4y^4 + 3xy^2 - 5*1*1) =>#

#2x^3y^5(6x^4y^4 + 3xy^2 - 5)#