Question

a) (x-1)*(x+4)-(x-1)²-3(x-1)
b) (a-b)*(x+3)+(b-a)*(2x-1)-(a-b)*(x+7)
c) (x+1)*(x-4)+(4-x)*(x+2)-x(x-4)
d) (2x-1)*(x+5)+(2x-1)²-2x²+x
e) (a-b)*(2x-3y)-(a-b)*(3x+4y)
f) (x-3)*(x+7y)+(3x+5y)*(3-x)

Answer 1

a) (x-1)(x+4)-(x-1)²-3(x-1)=
= (x-1)(x+4-x+1-3)=
= 2 (x-1)

b) (a-b)(x+3)+(b-a)(2x-1)-(a-b)(x+7)=
= (a-b)(x+3)-(a-b)(2x-1)-(a-b)(x+7)=
= (a-b)(x+3-2x+1-x-7)=
= (a-b)(-2x-3)

c) (x+1)(x-4)+(4-x)(x+2)-x(x-4)=
= (x+1)(x-4)-(x-4)(x+2)-x(x-4)=
= (x-4)(x+1-x-2-x)=
= (x-4)(-1-x)

d) (2x-1)(x+5)+(2x-1)²-2x²+x=
= (2x-1)(x+5)+(2x-1)²-x(2x-1)=
= (2x-1)(x+5+2x-1-x)=
= (2x-1)(2x+4)=
= 2(2x-1)(x+2)

e) (a-b)(2x-3y)-(a-b)(3x+4y)=
= (a-b)(2x-3y-3x-4y)=
= (a-b)(-x-7y)

f) (x-3)(x+7y)+(3x+5y)(3-x)=
= (x-3)(x+7y)-(3x+5y)(x-3)=
= (x-3)(x+7y-3x-5y)=
= (x-3)(-2x+2y)=
= 2(x-3)(y-x)