<s>[INST] Finding (or rather expanding) the product $(5-xy)(3+xy)$ 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.
 [/INST] $$ \begin {align*} (5 - xy)(3 + xy) &= 5 \cdot 3 + 3 \cdot (-xy) + 5 \cdot (xy) + (-xy) \cdot (xy) \\&= 15 - 3xy + 5xy - (xy)^2 \\&= 15 + 2xy - x^2y^2. \end {align*} $$Hope that makes sense!
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