# squared with a negative number

So I am trying to understand this formula.

I get that 7 squared is 7 * 7 = 49; However the () scares me, I get that there are rules for what to do first but they always confuse me. How does (-2) squared become 4 I know that two of - becomes a + somehow, could someone write out the simple formula for (-2) becoming 4

• What is $(-2)\cdot (-2)$? – Xander Henderson Jul 1 '18 at 23:13

The parentheses mean do this first, so you negate the $2$ before squaring. We have $$(-2)^2=(-2)\cdot (-2)=4$$
• Yes. I thought having the parentheses emphasized that we are multiplying $-2$ by $-2$. Without the parentheses in the original problem most people would read $-2^2$ as $-(2^2)=-4$ or at least be worried that was what was intended. – Ross Millikan Jul 1 '18 at 23:20
• Pretty much, @Varga Although we need the left-hand side of $(-2)^2 = -2\cdot -2 = 4$ to help avoid ambiguities, at a minimum, because, given the usual precedence of operators, as Ross notes, when we write only $-2^2$, it is to be evaluated as $-(2^2)= -(4) = -4$. So $(-2)^2 \neq -2^2$, but on the right hand side, we can certainly write $(-2)^2 = -2 \cdot -2$. – Namaste Jul 1 '18 at 23:28