1.(a+b+c)^2-(a-b-c)^22.25(x-y)^2-16(x+y)^23.x^4-81x^2y^24.x^2(x-y)+y^2(y-x)5.(a-b)(x-y)+(b-a)(x+y)

Question

1.(a+b+c)^2-(a-b-c)^2
2.25(x-y)^2-16(x+y)^2
3.x^4-81x^2y^2
4.x^2(x-y)+y^2(y-x)
5.(a-b)(x-y)+(b-a)(x+y)

Answer 1

1.(a+b+c)^2-(a-b-c)^2
=[(a+b+c)+(a-b-c)][(a+b+c)-(a-b-c)]
=2a*2(b+c)
=4a(b+c)
2.25(x-y)^2-16(x+y)^2
=[5(x-y)+4(x+y)][5(x-y)-4(x+y)]
=(9x-y)(x-9y)
3.x^4-81x^2y^2
=x^2(x^2-81y^2)
=x^2(x+9y)(x-9y)
4.x^2(x-y)+y^2(y-x)
=x^2(x-y)-y^2(x-y)
=(x^2-y^2)(x-y)
=(x+y)(x-y)^2
5.(a-b)(x-y)+(b-a)(x+y)
=[(a-b)+(b-a)]x+[(b-a)-(a-b)]y
=0+2(b-2a)y
=2(b-a)y