Answer:
<u>2x(2+3y)</u>
Step-by-step explanation:
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 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! :)
