12. Combining and arranging terms
Exercises
Identical terms
Two terms are identical if they have exactly the same variable part. The constants are also similar.
Only identical terms can be combined in addition and subtraction. When combining identical terms, the sum or difference of the coefficients is calculated and the letter part remains the same.
Example 1
Simplify the expressions if possible.
| a) | [[$ 17 \text{ €} + 4 \text{ €} = 21 \text{ €} $]] | |
| b) | [[$ 150 \text{ m} -35 \text{ m} = 115 \text{ m} $]] | |
| c) | [[$ 6x+9x=15x $]] | |
| d) | [[$ 18 \text{ cm} + 101 \text{ €} $]] | Cannot be combined, because the terms have different letters. |
| e) | [[$ 5a-3b $]] | Cannot be combined, because the terms have different letters. |
Example 2
Simplify the expressions.
Arranging the terms of polynomial
The terms of a polynomial are usually arranged in alphabetical order according to their letter parts, so that the exponents of the letter parts decrease from left to right. The standard term is written last.
Example 3
Arrange the polynomials.a) [[$ -3a^2 + 6 + a^4 = a^4 -3a^2 +6 $]]
b) [[$ ab +2a^3 -4b +b^2 = 2a^3 +ab +b^2 -4b $]]