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I've been recently studiying an Algebra course online, and right now on a review test this expression must be simplified: $$(-2x)^2(-y)^3$$ I distributed the exponent to the terms part and simplified it to $$(4x^2)(-y^3)$$ My question here, it seems to be wrong on the top part simplification as the correct answer that the page graded me was $$(-4x^2)(+y^3)$$ So that means that the result I got before should be multiplied by $-1$ to get this answer, why is this? Isn't my answer exactly the same as this one? Is it part of a standard form to present this? Does the $y$ value must be always positive?

Thanks for the help guys!

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Your way is fine, the second way, without parentheses $-4x²y³$, just looks nicer. –  GPerez Jan 14 at 23:18
    
@GPerez Alright! Thanks alot! Was going crazy about it. –  Joel Hernandez Jan 14 at 23:20

1 Answer 1

up vote 2 down vote accepted

Yes, we have

$(-2x)^2(-y)^3\ =\ (-2x)(-2x)(-y)(-y)(-y)\ =\ -4x^2y^3$

because there is an odd number (five) of sign switches altogether: $$(-1)^5=(-1)(-1)(-1)(-1)(-1)=-1\,.$$

Anyway, the expressions $(-4x^2)(y^3)$ and $(4x^2)(-y^3)$ coincide, so both solutions are correct.

I think, it might be some kind of 'standard form' as you guessed, namely that we prefer to put the '$-$' sign in front of the expression. (But this usage of parenthesis is rather unusual.)

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Oh, thank you, I was trying to understand completely your past answer and could not find a reusable logic from it.. This makes much more sense now. Thank you. –  Joel Hernandez Jan 14 at 23:19

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