Question

Factor xy+qr-xr-qy using grouping method

Answer 1

We are given the following expression:

$xy+qr-xr-qy$

We will associate the terms that have common factors, like this:

$(xy-xr)+(qr-qy)$

Now we take the common factor for each of the parenthesis:

$x(y-r)+q(r-y)$

Since each parenthesis has a common factor but with inverted signs, we will take -1 as a common factor in the second parenthesis, we get:

$x(y-r)-q(y-r)$

Now we can take "y-r" as a common factor for the entire expression:

$(y-r)(x-q)$

And thus we have factored the expression.