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Factor the follwing:

 

 5ax^2 + x^3 - 5a - x

 

a^2 - b^2 + 12b - 36 

 

3x^3 - x^2y +6x^2y - 2xy^2 + 3xy^2 - y^3


 

 Aug 29, 2018
 #1
avatar+974 
+3

1. 

 

\(5ax^2 + x^3 - 5a - x\\ =(5ax^2-5a)+(x^3-x)\\ =5a(x^2-1)+x(x^2-1)\\ =(x^2-1)(5a+x)\\ =(x-1)(x+1)(5a+x)\\\)

2. 


\(a^2 - b^2 + 12b - 36\\ =a^2 - (b^2 - 12b + 36)\\ =a^2 - (b - 6)^2\\ =[a - (b - 6)][a + (b - 6)]\\ =(a - b + 6)(a + b - 6)\)

 

3.

 

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

 

I hope this helped,

 

Gavin

 Aug 29, 2018

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