factorise this expression 4x+6xy why is the answer 2x(2+3y) and not 2(2x+3xy)

Question

plz explain is it ok if i use my version will the examiners still accept it

Answer 1

• To factorize an expression is to find factors such that when you multiply all of them you retrieve the original expression. Our given expression has two terms 4x and 6xy. 4x can be written as 2 (2x) and 6xy can be written as 3y (2x). 2x is a factor common to both terms 4x and 6xy. We factor out 2x. The proposed answer 2x(2+3y) is correct. 
• It's not ok to use your version 2(2x+3xy) because you still can factorize (2x+3xy).Indeed, the expression 2x+3xy, derived from 4x+6xy, can be written as x(2+3y). The examiner is likely to consider that you didn't finish the task and give you only partial credit if your final answer is 2(2x+3xy).
• The answer 2x(2+3y) has three factors, namely, 2, x, (2+3y) and we cannot factorize any further. The answer 2(2x+3xy) has two factors 2 and (2x+3xy); the latter (2x+3xy) can be factorized! [ x(2+3y)]. Get into the habit of factorizing completely and enjoy full credit for your answer! :) 

Answer 2

When using factoring to simplify an expression like this, both numbers and variables are included in the greatest common factor. When you first looked at the expression, you immediately noticed that both the 4 and 6 are divisible by 2. That's why you factored out the '2' and placed it outside the parenthesis.

Now ask yourself, are there any variables or letters that are shared by all parts of the expression, and there is! Both the 4x and the 6xy have an 'x' variable, just as it can be said that the numbers both have a '2' in them. We treat variables the same way - we factor it out and place it outside the parenthesis.

Hence 4x+6xy factors to 2x(2+3y). Your answer, 2(2x+3xy), may receive partial credit. It just isn't fully factored yet.

Keep in mind that when you have expressions that contain both numbers and variables, factoring may include just variables [ex: 5x+8xy -> x(5+8y)], just numbers [ex: 4x-2 -> 2(2x-1)], or both as your problem did. Be sure to check both!