Question

(1)ab(x+y)(x-y)-xy(a+b)(a-b) (2)x^4+x^2-2ax+1-a^2 (3)a^4-a^2

Answer 1

ab(x+y)(x-y)-xy(a+b)(a-b)

=ab(x^2-y^2)-xy(a^2-b^2)

=abx^2-aby^2-xya^2+xyb^2

=ax(bx-ay)-by(ay-bx)

=ax(bx-ay)+by(bx-ay)

=(ax+by)(bx-ay)

x^4+x^2-2ax+1-a^2

=x^4+2x^2+1-(x^2-2ax+a^2)

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

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

a^4-a^2+4a-4

=a^4-(a^2-4a+4)

=a^4-(a-2)^2

=(a^2+a-2)(a^2-a+2)

=(a+2)(a-1)(a^2-a+2)