Terms with the same variable part are called like terms
because they look ‘alike’ as far as the variable part is concerned.
The phrase like terms can refer to two or more terms.
Thus,
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$\,2x\,$ and $\,-5x\,$ are like terms.
In each term, the variable part is $\,x\,$.
Also,
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$\,x^2\,$,
$\,\frac{1}{3}x^2\,$, and
$\,(4.2)x^2\,$ are like terms.
In each term, the variable part is
$\,x^2\,$.
Only like terms can be combined, and they are combined by adding the coefficients.
For example,
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$\,2x + 5x = (2 + 5)x = 7x\,$ and
$\,7y - 4y = (7 - 4)y = 3y\,$.
You might want to think of these in concrete terms:
Two x-rays plus five x-rays is seven x-rays.
Seven yo-yos minus four yo-yos is three yo-yos.
Terms that are not like terms cannot be combined.
For example, there is no simpler way to write
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$\,2x + 5y\,$ or
$\,y - 2y^2\,$.
Terms must be written in the order the term types appear, from left-to-right, in the original expression.
Use the ‘ ^ ’ key for exponents.