# Thread: factoring cubed function

1. ## factoring cubed function

(x+(DELTAX))^3

i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help

2. Originally Posted by maybnxtseasn
(x+(DELTAX))^3

i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
It is factored. Do you mean you want to multiply it?

One way: $\displaystyle (x+\Delta x)^2= (x+ \Delta x)(x+ \Delta x)= x^2+ (\Delta x)(x)+ x(\Delta x)+ (\Delta x)^2$
$\displaystyle = x^2+ 2x\Delta x+ (\Delta x)^2k$

and then $\displaystyle (x+ \Delta x)^3= (x+ \Delta x)(x+ \Delta x)^2$$\displaystyle = (x+ \Delta x)(x^2+ 2x\Delta x+ (\Delta x)^2)$$\displaystyle = x(x^2)+ \Delta x(x^2)+ x(2x\Delta x)+ \Delta x(2x\Delta x)+ x(\Delta x)^2+ \Delta x(\Delta x)^2$
$\displaystyle = x^2+ 3x^2\Delta x+ 3x(\Delta x)^2+ (\Delta x)^3$

Quicker way: if you know the general formula $\displaystyle (a+ b)^3= a^3+ 3a^2b+ 3ab^2+ b^3$, use that with a= x and $\displaystyle b= \Delta x$ to get the same thing.
The text contains a mathematical question about factoring a cubed function, and the answer is provided in the form of a step-by-step explanation of how to expand the expression.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
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# Thread: factoring cubed function

1. ## factoring cubed function

(x+(DELTAX))^3

i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help

2. Originally Posted by maybnxtseasn
(x+(DELTAX))^3

i feel dumb but i totally forgot how to factor this so i can actually work with it in my calc class :O? any help
It is factored. Do you mean you want to multiply it?

One way: $\displaystyle (x+\Delta x)^2= (x+ \Delta x)(x+ \Delta x)= x^2+ (\Delta x)(x)+ x(\Delta x)+ (\Delta x)^2$
$\displaystyle = x^2+ 2x\Delta x+ (\Delta x)^2k$

and then $\displaystyle (x+ \Delta x)^3= (x+ \Delta x)(x+ \Delta x)^2$$\displaystyle = (x+ \Delta x)(x^2+ 2x\Delta x+ (\Delta x)^2)$$\displaystyle = x(x^2)+ \Delta x(x^2)+ x(2x\Delta x)+ \Delta x(2x\Delta x)+ x(\Delta x)^2+ \Delta x(\Delta x)^2$
$\displaystyle = x^2+ 3x^2\Delta x+ 3x(\Delta x)^2+ (\Delta x)^3$

Quicker way: if you know the general formula $\displaystyle (a+ b)^3= a^3+ 3a^2b+ 3ab^2+ b^3$, use that with a= x and $\displaystyle b= \Delta x$ to get the same thing.
user
The text contains a mathematical question about factoring a cubed function, and the answer is provided in the form of a step-by-step explanation of how to expand the expression.

TYPE: SINGLE_QUESTION_WITH_ANSWER