# Simplifying an algebra question

• evosy1978
He could have done it all in one step:$$V = x^2 \cdot \frac{75-x^2}{2x} = \frac{x^2(75-x^2)}{2x} = \frac{x(75-x^2)}{2} = \frac{x(75) - x(x^2)}{2} = \frac{x \cdot 75 - x^3}{2} = \frac{75x - x^3}{2}$$Note that the 3rd step here is just the first step in the 3-step process I had in my last post. The point is: you can "bring the 2x downstairs" by dividing by
evosy1978
Hello,

Ive was reading my literature today and it showed me some algebra, which i did not understand how it went from one step to the next...

What was done to simplify
V= x^2 ( 75-x^2 / 2x ) into V= x/2 ( 75-x^2 )

& then what was done to simplify ^^^

V= x/2 ( 75-x^2 ) into V= 1/2 ( 75x-x^3 )

(for anyone interested the above has now been differentiated)

I would now like to know when finding x how they go from
1/2 ( 75-3x^2 ) = 0 to this 75 = 3x^2

Thanks for any help. I know I'm missing something simple here?

evosy1978 said:
Hello,

Ive was reading my literature today and it showed me some algebra, which i did not understand how it went from one step to the next...

What was done to simplify
V= x^2 ( 75-x^2 / 2x ) into V= x/2 ( 75-x^2 )
You mean V= x^2((75- x^2)/(2x)). That is, the entire "75- x^2" is divided by 2x. You can factor 1/(2x) out to get (x^2/2x)(75- x^2)= (1/2)(x)(75- x^2).

& then what was done to simplify ^^^

V= x/2 ( 75-x^2 ) into V= 1/2 ( 75x-x^3 )
Now multiply the "x" back into the 75- x^2: x/2= (1/2)(x)(75- x^2)= (1/2)(75(x)- x^2(x))= (1/2)(75x- x^3).

(for anyone interested the above has now been differentiated)

I would now like to know when finding x how they go from
1/2 ( 75-3x^2 ) = 0 to this 75 = 3x^2
Multiply both sides by 2 to get 75- 3x^2= 0
then add 3x^2 to both sides: 75= 3x^2

Thanks for any help. I know I'm missing something simple here?
Although you don't mention it, an obvious next thing to do is to divide both sides by 3:
25= x^2. What you do now depends upon what the question is! If it is to solve for x, take the square root of both sides.

Ok, thanks for taking the time to reply, just to let you know it can sometimes take time for things to "click in my head" lol.. I am still confused, so can I break it down and show you where I am at...
HallsofIvy said:
That is, the entire "75- x^2" is divided by 2x. You can factor 1/(2x) out to get (x^2/2x)(75- x^2)= (1/2)(x)(75- x^2).
I understand the last bit as you have canceled out one of the x's from the top and bottom of the fraction.
Im confused as to where the part in red 1/(2x) came from?
I also don't understand why the 2x disappears from under the 75-x^2 and then appears under the x^2? Thanks

Last edited:
evosy1978 said:
Im confused as to where the part in red 1/(2x) came from?
I also don't understand why the 2x disappears from under the 75-x^2 and then appears under the x^2?

It's like this:

##V= x^2 (\frac{75-x^2}{2x})=\frac{1}{2x}x^2(75-x^2)=\frac{x}{2}(75-x^2)##

Here's a couple of the rules for working with fractions and multiplications:
$$\frac 2 3 = 2 \cdot \frac 1 3$$
$$2 \cdot 3 \cdot 4 = 4 \cdot 2 \cdot 3$$
$$\frac {3 \cdot 2} {5 \cdot 2} = \frac 3 5$$
These are the rules MrWarlock applied.

## What is simplifying an algebra question?

Simplifying an algebra question involves reducing a mathematical expression or equation to its simplest form by combining like terms, removing unnecessary parentheses, and using the order of operations.

## Why is it important to simplify an algebra question?

Simplifying an algebra question allows us to solve the equation or expression more easily and accurately. It also helps to understand the underlying concepts and relationships between variables.

## What are the steps involved in simplifying an algebra question?

The steps involved in simplifying an algebra question are: 1) Combine like terms, 2) Remove parentheses, 3) Use the distributive property, 4) Simplify exponents, and 5) Apply the order of operations.

## Can I use different methods to simplify an algebra question?

Yes, there are various methods that can be used to simplify an algebra question, such as factoring, using the distributive property, and using the FOIL method (First, Outer, Inner, Last).

## Are there any common mistakes to avoid when simplifying an algebra question?

Yes, some common mistakes to avoid when simplifying an algebra question are: 1) Forgetting to distribute a negative sign, 2) Combining unlike terms, 3) Making errors when simplifying exponents, and 4) Not following the correct order of operations.

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