1 Addition and subtraction of like terms

Like terms are multiples of the same quantity. For example $5y$ , $17y$ and $\frac{1}{2}y$ are all multiples of $y$ and so are like terms. Similarly, $3x^2$ , $-5x^2$ and $\frac{1}{4}{x}^2$ are all multiples of $x^2$ and so are like terms.

Further examples of like terms are:

$kx$ and $\ell x$ which are both multiples of $x$ ,

$x^{2}y$ , $6x^{2}y$ , $-13x^{2}y$ , $-2y{x}^2$ , which are all multiples of $x^{2}y$

$ab{c}^2$ , $-7ab{c}^2$ , $kab{c}^2$ , are all multiples of $ab{c}^2$

Like terms can be added or subtracted in order to simplify expressions.

Example 27

Simplify $5x-13x+22x$ .

Solution

All three terms are multiples of $x$ and so are like terms. The expression can be simplified to $14x$ .

Example 28

Simplify $5z+2x$ .

Solution

$5z$ and $2x$ are not like terms. They are not multiples of the same quantity. This expression cannot be simplified.

Task!

Example 29

Simplify $2x^2-7x+11x^2+x$ .

Solution

$2x^2$ and $11x^2$ , both being multiples of $x^2$ , can be collected together and added to give $13x^2$ .

Similarly, $-7x$ and $x$ can be added to give $-6x$ .

We get $2x^2-7x+11x^2+x=13x^2-6x$ which cannot be simplified further.

Task!

Example 30

Simplify $3a^{2}b-7a^{2}b-2b^2+a^2$ .

Solution

Note that $3a^{2}b$ and $7a^{2}b$ are both multiples of $a^{2}b$ and so are like terms. There are no other like terms. Therefore

$3a^{2}b-7a^{2}b-2b^2+a^2=-4a^{2}b-2b^2+a^2$

Interactive Exercises

Click here to open in a new window