Factor $$x^2+10x+25-9y^2$$
The solution is
$$(x+5-3y)(x+5+3y)$$
I understand how to factor when there is only one variable $x$ but I am not sure how to complete this problem with the additional variable $y$.
$\endgroup$3 Answers
$\begingroup$Consider $x$ only: $x^2+10x+25=(x+5)^2$, then you can use it with the whole expression:
$$x^2+10x+25 - 9y^2=(x+5)^2-(3y)^2=(x+5-3y)(x+5+3y)$$
Because $a^2-b^2=(a-b)(a+b)$, you only need to substitute $a=x+5$ and $b=3y$.
$\endgroup$ 3 $\begingroup$Note that$$a^2-b^2=(a-b)(a+b)$$Now put that$$a=x+5$$$$b=3y$$
$\endgroup$ $\begingroup$The given equation can be treated like quadratic in y assuming x to be constant.
Then y=$\frac{\pm \sqrt{36(x^2+10x+25)}}{18}$$$3y=(x+5) \,\,or\,\,3y=-(x+5)$$
$\endgroup$ 3
