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I get 69 when I calculate this, but my calculator says it's 29. I've gone over this several times and can't figure out why I'm wrong. I'm also not entirely sure if I've used the calculator properly.

What answer is correct, and any idea where I'm heading wrong here?

BLAZE
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Julian Nikolay Krogh-Fredrikse
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  • Okay so $(-2-2)^2$ gives me $8$. $-(-2+3)(-2-3)$ gives me $5$. And $-4(-2^2+2)$ gives me $8^2-8$ which is $56$.

    Add these together and I get $69$.

     – Julian Nikolay Krogh-Fredrikse Oct 12 '15 at 21:37
  • You didn't use the parentheses properly in the very first expression, $(-2-2)^2$ is not $8$. – hardmath Oct 12 '15 at 21:40
  • I thought that gave me (4+4), am I supposed to solve the inside of the parantheses before I apply the exponentiation? Did not know that.. – Julian Nikolay Krogh-Fredrikse Oct 12 '15 at 21:41
  • Yes, that's the purpose of parentheses. – hardmath Oct 12 '15 at 21:42
  • Also, It seems that you did like $-4\times (-2^2)=8^2$. This is wrong. Since $-2^2=-(2^2)=-4$, we have $-4\times (-2^2)=-4\times (-4)=16$. – mathlove Oct 12 '15 at 21:45
  • Yeah it appears as if I've made the same mistake throughout the entire calculation.

    I mean I did get the right answer for $-(-2+3)(-2-3)$ by simply adding both numbers with both numbers and not solving the parentheses first, which was $5$, but I guess it gets messed up once exponentials are involved.

     – Julian Nikolay Krogh-Fredrikse Oct 12 '15 at 21:48
  • No, it is the same principle: do everything inside the parentheses (which here is adding/subtracting both pairs of numbers) before doing the operation outside the parentheses (which here is either applying the unary minus or doing the multiplication, which can be done in either order with equal result). – hardmath Oct 12 '15 at 23:58

2 Answers2

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You have used you calculator properly. It is

$$(-2-2)^2=(-4)^2=16,$$ $$(-2+3)(-2-3)=1\cdot (-5)=-5,$$ and $$-4(-2^2+2)=-4(-4+2)=-4(-2)=8.$$ Thus, you get

$$16-(-5)+8=16+5+8=29.$$

mfl
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I believe your calculator is correct.

\begin{align*} &(-2-2)^2-(-2+3)(-2-3)-4(-2^2+2)\\ &=(-4)^2-(1)(-5)-4(-4+2)\\ &=(16)-(-5)+16-8\\ &=16+5+16-8\\ &=21+8\\ &=29 \end{align*} Note that $-2^2=-4$ whereas $(-2)^2=4$.