Where Did I Go Wrong in Simplifying this Algebraic Expression?

[uperkurk]

Simplify $-d^2+[9d+(2-4d^2)]$

$-d^2+[9d+(2-4d^2)]$

$d^2[-9d-2+4d^2]$

$d^2+4d^2-9d-2$

$5d^2-9d-2$

but wolfram says the answer is

$-5d^2-9d+2$

What did I do wrong?

 

[HallsofIvy]

Simplify $-d^2+[9d+(2-4d^2)]$

$-d^2+[9d+(2-4d^2)]$

$d^2[-9d-2+4d^2]$

Here is your error- first, you have dropped the "+" in front of the "[" but that may be just a typo- more importantly you have distributed the "-" in front of $d^2$ into the $[9d+(2- 4d^2)$. Where you were supposed to have -A+ B, you have A- B.

$d^2+4d^2-9d-2$

$5d^2-9d-2$

but wolfram says the answer is

$-5d^2-9d+2$

What did I do wrong?

 

[marie.phd]

−d2+[9d+(2−4d2)]

−d2+9d+2−4d2

-5d2 + 9d − 2

 

[Mark44]

Without any indication that the 2 in d2 is an exponent, what you have here is close to meaningless.

−d2+[9d+(2−4d2)]

−d2+9d+2−4d2

-5d2 + 9d − 2

At a minimum, use ^ to indicate exponents, and = for expressions that are equal, like this:

-d^2 + [9d + (2 − 4d^2)]
= -d^2 + 9d + 2 - 4d^2
= -5d^2 + 9d + 2

Even better is to write exponents that actually look like exponents, using the exponent feature that is available when you click Go advanced.

-5d² + 9d + 2

 

[HallsofIvy]

Simplify $-d^2+[9d+(2-4d^2)]$

$-d^2+[9d+(2-4d^2)]$

$-d^2- 4d^2= -5d^2$
You seem to be under the impresion that adding two negatives gives a positive. That is not true. That rule only holds for multiplication and division.

$d^2[-9d-2+4d^2]$

$d^2+4d^2-9d-2$

$5d^2-9d-2$

but wolfram says the answer is

$-5d^2-9d+2$

What did I do wrong?