Collecting Like Terms

Polynomials can can be simplified by combining like terms, or terms with the same variables and exponents.

For example, \( a^2b \) and \( -4a^2b\) would be considered like terms and can be combined. To collect the terms, simply add or subtract the coefficients:

Below are some more examples of terms that are like and unlike:

Term	Like Term	Unlike Term
\(a\)	\(3a, -2a, \cfrac{1}{3}a\)	\(a^2, \cfrac{1}{a}, \sqrt{a}\)
\(a^2\)	\(-5a^2,\cfrac{1}{4}a^2, 0.6a^2\)	\(\cfrac{1}{a^2}, \sqrt{a^2}, a^3\)
\(ab\)	\(7ab,0.2ab,\cfrac{2}{3}ab,-ab\)	\(a^2b,\cfrac{1}{ab}, \sqrt{ab}\)
\(ab^2\)	\(4ab^2, \cfrac{ab^2}{7},0.4ab^2,-ab^2\)	\(a^2b,ab,\sqrt{ab^2},\cfrac{1}{ab^2}\)

Example

Simplify the expression \((6k - 4) + (2k + 4)\).

We can simplify \( (6k - 4) + (2k + 4) \) using the following steps.

First, we can remove the brackets and identify the like terms:

\(= \textcolor{blue}{6k} - 4 + \textcolor{blue}{2k} + 4 \)

Next, we can identify the like terms and reorder them:

\(= \textcolor{blue}{6k} + \textcolor{blue}{2k} + 4 - 4 \)

Finally, we can collect the like terms:

\(= 8k\)

Therefore, we can determine that the expression simplified is \(8k\).

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\( (x^2 + 2x + 1) + (2x^2 + 4) \)

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\( −4x + 3x^2 −7 + 9x- 12x^2 −5x^4 \)

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