Questions: Factor by first grouping the appropriate terms. x^2-y^2+x+y

Solution Steps

To factor the expression \(x^2 - y^2 + x + y\) by grouping, we can rearrange and group the terms in a way that allows us to factor them easily. We can group the terms as \((x^2 + x)\) and \((-y^2 + y)\), then factor each group separately. Finally, we combine the factored groups to find the overall factored form.

We start with the expression: \[ x^2 - y^2 + x + y \] We can rearrange it as: \[ x^2 + x - y^2 + y \]

Next, we group the terms: \[ (x^2 + x) + (-y^2 + y) \]

Now, we factor each group: \[ x(x + 1) - y(y - 1) \] This can be rewritten as: \[ (x + y)(x - y + 1) \]

Final Answer