Finding (or rather expanding) the product $(5-xy)(3+xy)$

Question

Given the product $(5-xy)(3+xy)$

I tried the following,

As we know, $(x+a)(x+b)=x^2+(a+b)x+ab$

Here $x$ is $xy$. But $xy$ has two signs$-$ and $+$.

How do I solve this.

Answer 1

$$ \begin {align*} (5 - xy)(3 + xy) &= 5 \cdot 3 + 3 \cdot (-xy) + 5 \cdot (xy) + (-xy) \cdot (xy) \\&= 15 - 3xy + 5xy - (xy)^2 \\&= 15 + 2xy - x^2y^2. \end {align*} $$Hope that makes sense!

Answer 2

You want to use the FOIL method.

You multiply the FIRST terms: $5 \cdot 3 = 15$
You multiply the OUTER terms: $5 \cdot xy = 5xy$
You multiply the INNER terms: $-xy \cdot 3 = -3xy$
You multiply the LAST terms: $xy \cdot -xy = -x^2y^2$

You add them all together: $15 + 5xy + -3xy + -x^2y^2 = 15 + 2xy - x^2y^2$

And you're done.