Harder Factorising - mathematical?

Question

x^4 + 12x^3y + 35x^2y^2

Answer 1

x^2(x+7y)(x+5y)

Answer 2

x^4 + 12x^3y + 35x^2y^2

First you should do is to get the common terms:

x^2= common to all

x^2 (x^2 + 12xy + 35y^2)

factor:

(x^2 + 12xy + 35y^2)

x^2 = (x)(x)

35y^2 = (7y)(5y)

(x^2 + 12xy + 35y^2)  = (x+7y)(x+5y)

now:

x^4 + 12x^3y + 35x^2y^2 = (x^2)(x+7y)(x+5y) ----> ans

Answer 3

x^4+7x^3y+5x^3y+35x^2y^2

=x^3(x+7y)+5x^2y(x+7y)

=(x^3+5x^2y)(x+7y)

=x^2(x+5y)(x+7y)

hence factors are

x^2 and x+5y  and  x+7y

Answer 4

x^4 + 12x^3y + 35x^2y^2

= x^2(x^2 + 12xy + 35y^2)

= x^2(x^2 + 7xy + 5xy + 35y^2)

= x^2(x + 7y)(x + 5y)