Combining like terms

[QuadraticKid]

I faced a problem that said x^2 + 4 + x + 3.
I thought that x^2 was x*x so you could add the x to it, but it was dead wrong. Can someone please explain to me why it can’t be combined?

 

[AvgStudent]

I faced a problem that said x^2 + 4 + x + 3.
I thought that x^2 was x*x so you could add the x to it, but it was dead wrong. Can someone please explain to me why it can’t be combined?

How did you combine [imath]x^2[/imath] and [imath]x?[/imath]

 

[Harry_the_cat]

\(\displaystyle x^2+x = x*x+x = x(x+1)\)

just like \(\displaystyle 7x+2x=x(7+2) = 9x\)

What you do, depends on the question and the context.

What did the actual question ask you to do?

If it asked you to simplify the expression \(\displaystyle x^2+4+x+3\) then the response would be \(\displaystyle x^2+x+7\), by collecting like terms.

\(\displaystyle x^2\) and \(\displaystyle x\) are not like terms.

 

[Dr.Peterson]

I faced a problem that said x^2 + 4 + x + 3.
I thought that x^2 was x*x so you could add the x to it, but it was dead wrong. Can someone please explain to me why it can’t be combined?

Since your title says "Combining like terms", you are supposed to add together like terms. Check your textbook or notes to see how that is defined; what it means is that terms have the same variable(s), with the same exponents. Here is one explanation:

Like Terms

Like terms are terms whose variables (and their exponents such as the 2 in x2) are the same. ... In other words, terms that are like each other.

www.mathsisfun.com

 

[Steven G]

x's are just place holders for numbers.
How would you combine 5^2 + 5? Do the same to x^2 + x.

 

[mmm4444bot]

How would you combine 5^2 + 5?

I'd evaluate the expression, using Order of Operations.

Do the same to x^2 + x.

How?



[imath]\;[/imath]

 

[Steven G]

I'd evaluate the expression, using Order of Operations.


How?



[imath]\;[/imath]

Just pushing the student to see for themselves that you can't combine 5^2 + 5 and x^2 + x as well.

 

[Khushi16M]

I faced a problem that said x^2 + 4 + x + 3.
I thought that x^2 was x*x so you could add the x to it, but it was dead wrong. Can someone please explain to me why it can’t be combined?

you can't add x^2 and x directly, as you have asked in the question x^2= x*x, so how it is possible to add both x*x and x directly. Let's take an example of
3^2+3
so is it possible for you to write it as 2(3^2) or 2(3)???
definitely not... right???
you have to perform it like:
3^2 i.e. 9
then add 3 to it. i.e.
9+3= 12
but in the given question, as x is a variable, not a number so you can't find its square directly. So, You can do one thing to add them-
Your equation is:
x^2+4+x+3
it can be written as
x^2+x+4+3
x(x+1)+7
According to me, This is the only way to add x^2 and x in this given equation.

 

[Deleted member 4993]

I faced a problem that said x^2 + 4 + x + 3.
I thought that x^2 was x*x so you could add the x to it, but it was dead wrong. Can someone please explain to me why it can’t be combined?

You could factor out 'x' from 'x^2 + x' and write:

x^2 + x = x * (x + 1)

 

[JeffM]

Combine like terms means two things: (a) combine numerals together using arithmetic, and (b) combine variables that have the same value but different coefficients using addition and subtraction.

3x + 5x = 8x.

We do not know what value x has, but in the same expression, it is always the same.

In general, however, [imath]x[/imath] and [imath]x^2[/imath] do not have the same value. For example [imath]5^2 = 25 \ne 5.[/imath] So you cannot combine them.

 

[lookagain]

Just pushing the student to see for themselves that you can't combine 5^2 + 5 ...

But they can be combined into one constant, 30. That shows how these integer
constants, for example, operate differently in combining like terms exercises.

 

[JeffM]

Do you want to simplify to a quadratic equation?

Technically, what the initial post was asking about is an expression rather than an equation. In elementary algebra, an equation is a statement, indicated by an = sign, that two expressions have the same numeric value.

Moreover, that initial expression already is a quadratic, but one that is not quite in standard form.