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Adding and Subtracting Like Terms
To combine like terms, do the following:
Determine which terms contain the same variable or groups of variables raised to the same exponent.
Add or subtract the numerical coefficients.
Attach the common variables and exponents.
For example, 3x + 6x can be simplified to (3+ 6) x = 9x
Example
If possible, simplify each of the following expressions.
Determine which terms contain the same variable or groups of variables raised to the same exponent: If we look at this equation we see that there are two terms which contain the variable a.
10a+ 10b– 3a
Add or subtract the numerical coefficients: We use the distributive property to rewrite the equation. Then perform the subtraction indicated, subtracting 3 from 10.
(10 – 3) a + 10b
Attach the common variables and exponents: We then display the final result from the subtraction.
7a + 10b
(2)5b^{2} + 8b^{3} = 5b^{2} + 8b^{3}
Determine which terms contain the same variable or groups of variables raised to the same exponent: While both terms have b's in them, they are raised to different powers, b^{2} and b^{3}. This means we cannot combine these two terms.
Determine which terms contain the same variable or groups of variables raised to the same exponent: If we look at this equation we see that there are two terms which contain the variable x^{2}y^{2}z.
3x^{2}y^{2}z – 5xyz + x^{2}y^{2}z
Add or subtract the numerical coefficients: We group these terms together and perform the addition indicated, adding 3 and 1 together.
(3 + 1)(x^{2}y^{2}z) – 5xyz
Attach the common variables and exponents: Here we have the final result.
4x^{2}y^{2}z – 5xyz
Combining like terms is crucial in solving equations. Thisis a procedure you will use often with algebraic expressions.