Question

А) X(y+z)-2y-2z Б) а(b+c)-b-c B) a(b-c)-4b+4c Г) a(a-b)-ac+bc

Answer 1

А) ху+хz-2y-2z=x(y+z)-2(y+z)=(x-2)(y+z)
Б) аb+ac-b-c=b(a-1)+c(a-1)=(b+c)(a-1)
В) ab-ac-4b+4c=b(a-4)-c(a-4)=(b-c)(a-4)
Г) а²-аb-ac+bc=a(a-b)-c(a-b)=(a-c)(a-b)

Answer 2

А) X(y+z)-2y-2z can be simplified as follows: X(y+z)-2y-2z = Xy + Xz - 2y - 2z = (X-2)y + (X-2)z = (X-2)(y+z)

Б) а(b+c)-b-c can be simplified as follows: a(b+c)-b-c = ab + ac - b - c = (a-1)b + (a-1)c = (a-1)(b+c)

B) a(b-c)-4b+4c can be simplified as follows: a(b-c)-4b+4c = ab - ac - 4b + 4c = (a-4)b + (4-a)c = (4-a)(c-b)

Г) a(a-b)-ac+bc can be simplified as follows: a(a-b)-ac+bc = a^2 - ab - ac + bc = a(a-b-c) - c(a-b) = (a-b)(a-c)