factorzion question

1. Factorize 2+4y + 7xy+4x - 2x^2 y

= (2+4y -xy ) + 8xy + 4x - 2yx^2

= (2 + 4y - xy) + 2x(4y + 2 - xy)

= (2x + 1)(4y - xy + 2)

2.Factorize x(x^3 +y^3) +xy(x^2 - y^2) + y^3 (x+y)

= (x+y)[ x(x^2 - xy + y^2) + xy(x - y) + y^3]

= (x+y)(x^3 + y^3)

= (x+y)^2 (x^2 - xy + y^2)

3. If x+ 1/x = 4 find the value of x^3 + 1/x^3

x^3 + 1/x^3

= (x + 1/x)(x^2 - x(1/x) + 1/x^2)

= 4(x^2 + 1/x^2 - 1)

= 4[(x + 1/x)^2 - 2x(1/x) - 1]

= 4(4^2 - 2 - 1)

= 4(13)

=52