SOLVING EQUATIONS BY ADDING SUBTRACTION MULTIPLY DIVIDE
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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.

1. 10a + 10b –3a
2. 5b2 + 8b3
3. 3x2y2z – 5xyz + x2y2z

1. 10a + 10b – 3a = 7a + 0b
2. 5b2 + 8b3 = 5b 2 + 8b3
3. 3x2y2z – 5xyz + x2y2z = 4x2 y2z – 5xyz

(1) 10a + 10b – 3a = 7a + 10b

To find the solution:

 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)5b2 + 8b3 = 5b2 + 8b3

 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, b2 and b3. This means we cannot combine these two terms. 5b2 + 8b3

(3) 3x2y2z – 5xyz + x2y2z= 4x2y2z – 5xyz

 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 x2y2z. 3x2y2z – 5xyz + x2y2z Add or subtract the numerical coefficients: We group these terms together and perform the addition indicated, adding 3 and 1 together. (3 + 1)(x2y2z) – 5xyz Attach the common variables and exponents: Here we have the final result. 4x2y2z – 5xyz

Combining like terms is crucial in solving equations. Thisis a procedure you will use often with algebraic expressions.