# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 2013-05-31 18:29:28

Hostible
Member
Registered: 2013-05-31
Posts: 5

### common mistake

Know that -a^2 means -1 x a^2 and not -a x -a.
The reason is that -a^2 has its coefficient as -1
Therefore -a x -a = a^2 and and not -a^2.
This symbol ^ implies exponent.

Last edited by Hostible (2013-05-31 18:30:49)

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## #2 2014-10-30 22:49:24

DeanPemberton
Member
From: USA
Registered: 2014-10-30
Posts: 20
Website

### Re: common mistake

Thank for explaining this exponential function here, I completely understand the equation. Here coefficient is different thing and variable is different.

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## #3 2021-05-15 04:50:47

mathland
Member
Registered: 2021-03-25
Posts: 444

### Re: common mistake

Hostible wrote:

Know that -a^2 means -1 x a^2 and not -a x -a.
The reason is that -a^2 has its coefficient as -1
Therefore -a x -a = a^2 and and not -a^2.
This symbol ^ implies exponent.

True but (-a)^2 is totally different.

We know that (-a)^2 = (-a)(-a) = a^2.

Let me see.

-[(a)(a)]

-(a^2)

-a^2

Agree?

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## #4 2022-08-18 08:17:30

Abbey78336
Member
Registered: 2022-08-15
Posts: 37

### Re: common mistake

It is not true !

-a^2 is not equal to -1×a^2

PROOF
if a=5 -a^2=(-5)^2=-5×-5=+25 but -1×a^2=-1×5^2=-1×25=-25
So -25 is not equal to +25

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## #5 2022-08-18 20:25:43

Bob
Registered: 2010-06-20
Posts: 10,476

### Re: common mistake

In the Uk we call it BODMAS. In the USA PEDMAS.

It's the set of priority rules for applying operations.

Parentheses or brackets first; then exponents (powers); then divide and multiply; and lastly addition and subtraction.

Thus, for example, 6 + 3 x 4 means 6 + (3 x 4) and not (6 + 3 ) x 4.  ie. Do the multiply before the addition.  All scientific calculators use these rules. (The early calculators could only do calculations as they were input.)

So the expression -a^2 requires that the power is evaluated (a^2) before the minus is applied; thus - a^2 = -(a^2)

So, is a = 5, the correct evaluation is - (5^2) = -25

If you want to force the subtract first then brackets should be used: (-a)^2 means -a times -a = +a^2

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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