What is the value of $x^2+y^2-z^2+2xy$ when $x=-3$, $y=5$, and $z=-4$?
We substitute the values of $x$, $y$, and $z$ to get $$(-3)^2+(5)^2-(-4)^2+2(-3)(5)=9+25-16-30=34-46=\boxed{-12}.$$
-12
Level 3
Algebra
Problem: What is the value of $x^2+y^2-z^2+2xy$ when $x=-3$, $y=5$, and $z=-4$?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the value of the expression $x^2 + y^2 - z^2 + 2xy$, we first substitute the given values of $x$, $y$, and $z$. 

Start with the values: $x = -3$, $y = 5$, and $z = -4$. 

Calculate $x^2$:
$x^2 = (-3)^2 = 9$.

Calculate $y^2$:
$y^2 = 5^2 = 25$.

Calculate $z^2$:
$z^2 = (-4)^2 = 16$.

Next, calculate $2xy$:
$2xy = 2 \cdot (-3) \cdot 5 = -30$.

Now, substitute these calculated values into the expression:
$9 + 25 - 16 - 30$.

Combine the values step-by-step:
First, add $9$ and $25$:
$9 + 25 = 34$.

Next, subtract $16$ from $34$:
$34 - 16 = 18$.

Finally, subtract $30$ from $18$:
$18 - 30 = -12$.

Thus, the final answer is $-12$.<|END_OF_LATENT|> The final answer is $-12$.