I was wondering why something like X^2 + 2x doesn't = 2x^3, yet via multiplication would...

It can be equal for specific values of x.

 

Have a think about

 

[math]x =0 [/math] and [math]x = \frac{1 \pm \sqrt{17}}{4}[/math].

for like terms in algebraic expressions, does the rule for only being able to add, multiple, divide and subtract go for just multiplication and division, just addition and subtraction or both ?

 

As in for something like 4x - 6y, can you only end up with 4x - 6y via subtraction because they are unlike, but for something like 4x * 6y, you could up with 24xy ? etc

[math]x^2 + 2 x = 2 x^3[/math]

 

[math]x^2 + 2 x - 2 x^3 = 0[/math]

 

one solution is [math]x = 0[/math]

Edited March 9, 201114 yr by khaled

As in for something like 4x - 6y, can you only end up with 4x - 6y via subtraction because they are unlike, but for something like 4x * 6y, you could up with 24xy ? etc

 

If I understand your question correctly then yes.

 

[math]4x -6y = 2(2 x - 3 y)[/math] is about as simple as it can get, assuming [math]x,y[/math] are independent variables. You can take the common factor of two "outside the bracket".

 

These questions are in elementary algebra, that is we understand x and y (etc.) to be variables that take their values in real numbers. You can also have systems where the variables are not real numbers or even just formal variables. I suggest you have a look at the Wikipedia entry on elementary algebra. I think it will help you.

ok cheers.

If [imath]x^2 + 2x = 2x^3[/imath] then

[imath]2x^3 - x^2 - 2x=0[/imath] so

[imath]2x^2 - x -2 =0[/imath].

 

Which by the Fundamental Theorem of Algebra, is only the case for at most two values of [imath]x[/imath].

This is basic algebra, and learned under combining like terms. As 4x and 6y have two different variables, so we can't combine them to make one term. But 4x*6y is a monomial (as number of terms of a polynomial are separated by + or - signs); hence we can multiply 4 and 6 to get 24 and we still have the monomial.