Calculate 6² - (-6)²: Comparing Positive and Negative Squares

Q: What's the difference between -6² and (-6)²?

The parentheses make all the difference! $ -6^2 = -(6^2) = -36 $ (negative of 6 squared), but $ (-6)^2 = 36 $ (negative 6 squared).

Q: Will 6² - (-6)² always equal zero?

Yes! For any number n, we have $ n^2 = (-n)^2 $ because squaring removes the negative sign. So $ n^2 - (-n)^2 = 0 $ always.

Q: How can I remember that negative squared becomes positive?

Think of it as "negative times negative equals positive". When you see $ (-6)^2 $, imagine writing it as $ (-6) \times (-6) $!

Q: What if the exponent was 3 instead of 2?

With odd exponents, the negative stays! $ (-6)^3 = (-6) \times (-6) \times (-6) = -216 $. So $ 6^3 - (-6)^3 = 216 - (-216) = 432 $.

Exponent Properties with Negative Base

$6^2-(-6)^2=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 First let's calculate the sign

00:06 Even power, therefore the sign will be positive

00:14 Any number minus itself always equals 0

00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$6^2-(-6)^2=$

Step-by-step solution

To solve the expression $6^2 - (-6)^2$ , let's follow these steps:

Step 1: Calculate $6^2$ .
$6^2 = 6 \times 6 = 36$ .
Step 2: Calculate $(-6)^2$ .
$(-6)^2 = (-6) \times (-6) = 36$ . Note that squaring a negative number results in a positive value.
Step 3: Subtract the results of Step 1 and Step 2.
$36 - 36 = 0$ .

Therefore, the solution to the problem is $0$ .

Final Answer

$0$

Key Points to Remember

Essential concepts to master this topic

Rule: Squaring any number, positive or negative, gives positive result
Technique: Calculate $(-6)^2 = (-6) \times (-6) = 36$
Check: Both $6^2$ and $(-6)^2$ equal 36, so 36 - 36 = 0 ✓

Common Mistakes

Avoid these frequent errors

Confusing negative with exponent
Don't calculate $(-6)^2$ as -36 = wrong answer of 72! The parentheses mean you square the negative number itself. Always remember: squaring a negative number gives a positive result.

Practice Quiz

Test your knowledge with interactive questions

$$ (-2)^7= $$

FAQ

Everything you need to know about this question

Why does (-6)² equal positive 36 instead of negative 36?

When you square a negative number, you're multiplying it by itself: $(-6)^2 = (-6) \times (-6)$ . Since negative times negative equals positive, the result is +36!

What's the difference between -6² and (-6)²?

The parentheses make all the difference! $-6^2 = -(6^2) = -36$ (negative of 6 squared), but $(-6)^2 = 36$ (negative 6 squared).

Will 6² - (-6)² always equal zero?

Yes! For any number n, we have $n^2 = (-n)^2$ because squaring removes the negative sign. So $n^2 - (-n)^2 = 0$ always.

How can I remember that negative squared becomes positive?

Think of it as "negative times negative equals positive". When you see $(-6)^2$ , imagine writing it as $(-6) \times (-6)$ !

What if the exponent was 3 instead of 2?

With odd exponents, the negative stays! $(-6)^3 = (-6) \times (-6) \times (-6) = -216$ . So $6^3 - (-6)^3 = 216 - (-216) = 432$ .

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