Find the value of c that would make the expression a perfect square. y^2+8y+c Show your work here

To make the expression $y^2 + 8y + c$ a perfect square trinomial, we need to find a value for 'c' such that the expression can be factored into the form $(y + a)^2$.<br /><br />Expanding $(y + a)^2$ gives us $y^2 + 2ay + a^2$.<br /><br />Comparing this with $y^2 + 8y + c$, we see that $2a = 8$, which means $a = \frac{8}{2} = 4$.<br /><br />Now, we can find the value of $c$ by substituting $a=4$ into $a^2$:<br />$c = a^2 = 4^2 = 16$.<br /><br />Therefore, the expression becomes $y^2 + 8y + 16$, which is equivalent to $(y+4)^2$.<br /><br />Final Answer: The final answer is $\boxed{16}$<br />