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)