Question

X(a+b)+y(a+b)= a(3x-2y)+b(3x-2y)= 3x(a-b)-5y(b-a)=

Answer 1

X(a+b)+y(a+b)=(a+b)(x+y)
a(3x-2y)+b(3x-2y)=(3x-3y)(a+b)
3x(a-b)-5y(b-a)=(a-b)(3x+5y)

Answer 2

Let's break down the given expressions step by step.

1. $X(a+b) + Y(a+b)$

   Here, factor out $(a+b)$ from both terms:

   $X(a+b) + Y(a+b) = (X+Y)(a+b)$

2. $A(3x-2y) + B(3x-2y)$

   Factor out $(3x-2y)$ from both terms:

   $A(3x-2y) + B(3x-2y) = (A+B)(3x-2y)$

3. $3x(a-b) - 5y(b-a)$

   Expand the terms inside the parentheses:

   $3x(a-b) - 5y(b-a) = 3ax - 3bx - 5by + 5ay$

   Now, rearrange the terms:

   $= (3a-5b)x + (-3b+5a)y$

Therefore, the given expressions can be simplified as follows:

$X(a+b) + Y(a+b) = (X+Y)(a+b)$

$A(3x-2y) + B(3x-2y) = (A+B)(3x-2y)$

$3x(a-b) - 5y(b-a) = (3a-5b)x + (-3b+5a)y$