+235 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
+981 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
