Question

Factor the following expression (7th grade):35x + 5xy

Answer 1

To factor is to apply the distribute property backwards.

The distributive property is:

$a(x+y)=ax+ay$

To factor is:

$ax+ay=a(x+y)$

Then, we need to find, in the two terms of the question, common factors of them.

We have:

$35x+5xy$

We have an x in both terms, then we can rewrite:

$35x+5xy=x(35+5y)$

Also, we can see that both term are divisible by 5. Then we can write:

$x(35+5y)=x(5\cdot7+5y)$

And now we can factor 5:

$x(5\cdot7+5y)=5x(7+y)$

Thus, the expression, factored is:

$5x(7+y)$