Factorise 4(x+y)(3a-b)+6(x+y)(2b-3a)
Please solve this fast.
Show your calculation.

(-3a+4b) (2x+2y)

Step-by-step explanation:

Expand.

4(x+y)(3a-b)+6(x+y)(2b-3a) = 4(3ax+3ay-bx-by) + 6(2bx+2by-3ax-3ay)

4(3ax+3ay-bx-by) + 6(2bx+2by-3ax-3ay)  = 12ax+12ay-4bx-4by+12bx+12by-18ax-18ay

Calculate like terms.

12ax+12ay-4bx-4by+12bx+12by-18ax-18ay = -6ax-6ay+8bx+8by

Factorise.

-6ax-6ay+8bx+8by = -3a(2x+2y) + 4b(2x+2y)

Factorise further.

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

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2