Question

factorise
(3x-y)^2 -(y+2x)^2

Answer 1

Hope this answer helps you:)

Answer 2

Given (3x - y)^2 - (y + 2x)^2.   ------- (1)


We know that (a-b)^2 = a^2 + b^2 - 2ab.

                 Then (3x - y)^2 = (3x)^2 + y^2 - 2 * 3xy

                                          = 9x^2 + y^2 - 6xy.   --------- (2)



We know that (a+b)^2 = a^2 + b^2 + 2ab

                 Then (y + 2x)^2 = y^2 + (2x)^2 + 2 * y * 2x

                                           = y^2 + 4x^2 + 4xy.  ----- (3)


Substitute (2) and (3) in (1), we get


(3x - y)^2 - (y + 2x)^2 = (9x^2 + y^2 - 6xy) - (4x^2 + y^2 + 4xy)

                                   = 9x^2 + y^2 - 6xy - 4x^2 - y^2 - 4xy

                                   = 5x^2 - 10xy.


Therefore (3x^2 - y)^2 - (y + 2x)^2 = 5x^2 - 10xy.


Hope this helps!