Question 1209149
For what real values of c is x^2 - 8x - 16x + c + 24x^2 the square of a binomial?
<pre>

First let's combine like terms:

{{{25x^2-24x+c}}}

So if it is to factor as the square of a binomial, there is 
some number a such that this is an identity:

{{{(5x + a)(5x + a)}}}{{{""=""}}}{{{25x^2-24x+c}}}

{{{25x^2+10ax+a^2}}}{{{""=""}}}{{{25x^2-24x+c}}}

So for them to be identical, we must have:

{{{10a=-24}}}} and {{{a^2=c}}}

{{{a=-24/10=-12/5}}} and {{{c=a^2=(-12/5)^2=144/25}}}

Answer: c = 144/25

Edwin</pre>