Help simplifying this algebraic expression please

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The discussion focuses on simplifying algebraic expressions, specifically addressing the simplification of terms like 3x^3 + 3/8x^3 and 9x^3/2 - 1/x^3/2. The correct simplification for the first expression is 3/2 x^3, achieved by recognizing the cube root of the constant multiplier. For the second expression, participants clarify that one cannot simply square individual terms and emphasize the importance of expanding brackets correctly to avoid confusion.

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homeworkhelpls
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14) here i tried 3x^3 + 3/8x^3 to to get 27/8x^3 but the answer is 3/2 x^3, why?
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15) here i did 9x^3/2 - 1/x^3/2 to get 9x^9/4 - 1/x^3/2 but that's not in the right form, how do i do it correctly?
 
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homeworkhelpls said:
View attachment 31519414) here i tried 3x^3 + 3/8x^3 to to get 27/8x^3 but the answer is 3/2 x^3, why?
Did you take the cube root of the constant multiplier?
homeworkhelpls said:
View attachment 31519615) here i did 9x^3/2 - 1/x^3/2 to get 9x^9/4 - 1/x^3/2 but that's not in the right form, how do i do it correctly?
That is not correct. You can not simply square the individual terms. Do you know what the general result of ##(a-b)^2## is? Multiply out the square to see what is right.
 
ok then for 15 i expanded the brackets and got 9x^3/2 -3x^0 - 3x^0 + x^-3/2, I am confused if -3x^0 is equal to -3 or 1, please explain
 
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FactChecker said:
Did you take the cube root of the constant multiplier?

That is not correct. You can not simply square the individual terms. Do you know what the general result of ##(a-b)^2## is? Multiply out the square to see what is right.
and for 14 i got it now after doing 3 x by cubed root of 3 x by x^3 all over 2 to get 3/2 x^3, thanks :)
 
homeworkhelpls said:
ok then for 15 i expanded the brackets and got 9x^3/2 -3x^0 - 3x^0 + x^-3/2, I am confused if -3x^0 is equal to -3 or 1, please explain
A product of both. ##-3x^0 = -3 \cdot x^0 = -3 \cdot 1 = -3##
 
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