Question

Descompuneti in factori:
a) 3x+18x^3y^3+27x^5y^6
b) x^2+2xy+y^2-z^2
c) 9-y^2-6yz-9z^2
d) a^3+a^2b-ab^2-b^3
e) 28x^3-8x^2y-7x+2y

Answer 1

a)3x+9x^3y^3+9x^3y^3+27x^5y^6 = 3x•(1+3x^2y^3) + 9x^3y^3•(1+3x^2y^3) =
(1+3x^2y^3)(3x+9x^3y^3)
b)(x+y)^2 - z^2 = (x+y+z)(x+y-z)
c)3^2 - (y+3z)^2 = (3+y+3z)(3-y-3z)
d)a^2•(a+b) - b^2•(a+b) = (a+b)(a^2 - b^2) = (a+b)^2(a-b)
e)7x•(4x^2 - 1) - 2y•(4x^2 - 1) = (4x^2 - 1)(7x-2y) =
(2x-1)(2x+1)(7x-2y)