Factorize the following

a) 4x- 2xy

b) 2x(x + 1) - 3(x + 1)

c) 6xy + 3a + 6ax + 3y

Explanations are welcome. Thanks

a) 4x- 2xy
Extract common factors.
Commons : 2 , x

Answer: 2x(2-y)

b) 2x(x + 1) - 3(x + 1)
Is simplified to 2x² -x - 3
Factor out, through trial and error.

Answer: (x+1)(2x-3)

c) 6xy + 3a + 6ax + 3y
Extract common factor: 3
= 3(2xy + a + 2ax + y)
Pair up common multiples that can help you factor.
= 3(2x+1)(y+a)

a. Factor out the 2x from both terms to get: 2x(2-y)
b. Foil, or distribute, the terms on the outside of the parentheses with the terms inside the parentheses to get: (2x^2+2x)-(3x+3). Then negate the second expression because of the - before it so we can combine like terms to get: 2x^2+2x-3x-3. Combine like terms to get: 2x^2-x-3. This can be factored as: (x+1)(2x-3).
c. Divide out the equation by 3 to get: 3(2xy+a+2ax+y)

a) 4x - 2xy
= 2x ( 2 - y) ans.
b) 2x( x+1) - 3 ( x+1)
= (x+1) (2x - 3) ans.
c) 6xy + 3a +6ax + 3y
= 6xy + 6ax+ 3y + 3a
= 3[ 2xy + 2ax + y + a ]
= 3 [2x ( y + a) + 1( y+ a) ]
= 3 ( 2x+1) ( y+a) ans.