Question

Write as a product of two polynomials

Answer 1

`(x-y)^(2) -a(y-x)`

Since the formula for
`(x-y)^(2) =x^(2) -2xy+y^2`.

So,

`x^(2)-2xy+y^(2) -a(y-x)`

=
`x^(2)-xy-xy+y^(2) -a(y-x)` (Breaking -2xy as -xy-xy)

=
`(x^(2)-xy)+(y^2-xy) -a(y-x)` (Making the group of terms)

=x(x-y) +y(y-x)-a(y-x) (Taking out the common factor)

=-x(y-x)+y(y-x)-a(y-x)

=(y-x)(-x+y-a)

=-(x-y)(-(x-y+a))

=(x-y)(x-y+a)