Like terms

Like terms are terms that contain the same series of letters and indices. Like terms in an equation may be added or subtracted from each other to simplify the equation.

Like terms are terms of an equation that contain the same variables, these can be summed together to make the whole equation more easier to handle

The y terms in the above equation can be combined to simplify the equation.

There are many like terms in this example can you spot them?

Example 1

Simplify the following expression `3x^2+y^3-x^2-y^3`

Note: By simplify they mean combine terms

`3x^2+y^3-x^2-y^3`

`3x^2-x^2+y^3-y^3`

`2x^2+0`

`2x^2`

Answer: `3x^2+y^3-x^2-y^3=2x^2`

Example 2

Simplify the following expression `3xy-4ac+5yx+4ac`

Note: By simplify they mean combine terms

`3xy-4ac+5yx+4ac`

`3xy+5yx+4ac-4ac`

`3xy+5yx+0`

Note: `5yx=5timesytimesx=5timesxtimesy=5xy`

`3xy+5xy`

`8xy`

Answer: `3xy-4ac+5yx+4ac=8xy`

Example 3

Simplify the following expression `2x^2+3x-5x^2-x+8`

Note: By simplify they mean combine terms

`2x^2+3x-5x^2-x+8`

`2x^2-5x^2+3x-x+8`

`-3x^2+2x+8`

Answer: `2x^2+3x-5x^2-x+8=-3x^2+2x+8`

Example 4

Expand and simplify the following `2x^2(4xy-5)-8yx^3+9x^2`

Note: By simplify they mean combine terms

`2x^2(4xy-5)-8yx^3+9x^2`

`8x^3y-10x^2-8yx^3+9x^2`

`8x^3y-8yx^3+9x^2-10x^2`

`cancel(8x^3y)-cancel(8yx^3)+9x^2-10x^2`

Answer: `2x^2(4xy-5)-8yx^3+9x^2=-x^2`