Question

how do I factor 6x-10y?

Answer 1

To factor an expression, find a common factor between each term or a set of terms in an expression. In your case, 6x-10y has a common factor of 2. This is known because 2 is the largest common factor of both 6 and 10, i.e. both 6 and 10 can be divided by 2.

To factor, we "pull" the common factor from both terms and set it out front of the expression.

\[6x-10y\]\[2(3x-5y)\]

By pulling this common factor out, we divide the numbers we pulled it from by that number, as seen above. If we "pull" 2 from 6, we are left with 3, because 6/2=3. It is the same with 10/2=5. Your expression no longer has any common factors, and is therefore factored.

We can check our answer by distributing 2 into the terms in the brackets, that is, multiply each term in the brackets by 2.



We multiply 3x by 2, and we get +6x. We then multiply -5y by 2 adn we get -10y. This leaves us with our original expression 6x-10y, meaning we factored correctly.