How do you factor 12x^7y^9+6x^4y^7-10x^3y^512x7y9+6x4y710x3y5?

1 Answer
Nov 28, 2016

2x^3y^5(6x^4y^4 + 3xy^2 - 5)2x3y5(6x4y4+3xy25)

Explanation:

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 xx the highest common value is x^3x3

For yy the highest common value is y^5y5

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)) =>2x3y5(6x73y95+3x43y755x33y55)

2x^3y^5(6x^4y^4 + 3x^1y^2 - 5x^0y^0) =>2x3y5(6x4y4+3x1y25x0y0)

2x^3y^5(6x^4y^4 + 3xy^2 - 5*1*1) =>2x3y5(6x4y4+3xy2511)

2x^3y^5(6x^4y^4 + 3xy^2 - 5)2x3y5(6x4y4+3xy25)