Math Is Fun Forum

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)

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.

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: 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.

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

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

How about -(a)^2?

Let me see.

-[(a)(a)]

-(a^2)

-a^2

Agree?

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,765

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

Reference: https://www.mathsisfun.com/operation-order-bodmas.html

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