Take Note Concept Summary: Properties for Simplifying Algebraic Expressions

Let a, b, and c represent real numbers.

Problem 5 Simplifying Algebraic Expressions

Combine like terms. What is a simpler form of each expression?

1. 7 x 2 + 3 y 2 + 2 y 2 − 4 x 2 7 , x squared , plus 3 , y squared , plus 2 , y squared , minus 4 , x squared
     7 x 2 + 3 y 2 + 2 y 2 − 4 x 2 Identify like terms. = 7 x 2 − 4 x 2 + 3 y 2 + 2 y 2 Commutative Property of Addition = ( 7 − 4 ) x 2 + ( 3 + 2 ) y 2 Distributive Property = 3 x 2 + 5 y 2 Combine like terms. table with 4 rows and 3 columns , row1 column 1 , , column 2 7 , x squared , plus 3 , y squared , plus 2 , y squared , minus 4 , x squared , column 3 cap identify like terms. , row2 column 1 , equals , column 2 7 , x squared , minus 4 , x squared , plus 3 , y squared , plus 2 , y squared , column 3 cap commutative cap property of cap addition , row3 column 1 , equals , column 2 open , 7 minus 4 , close . x squared , plus . open , 3 plus 2 , close . y squared , column 3 cap distributive cap property , row4 column 1 , equals , column 2 3 , x squared , plus 5 , y squared , column 3 cap combine like terms. , end table

   Think

   Are 7 x 2 7 , x squared  and 3 y 2 3 , y squared  like terms?

   No; they have different variables.

2. − ( 3 k + m ) + 2 ( k − 4 m ) negative open 3 k plus m close plus 2 open k minus 4 m close

   − 3 k − m + 2 k − 8 m Opposite of a Sum and Distributive Property = − k − 9 m Combine like terms . table with 2 rows and 2 columns , row1 column 1 , negative 3 k minus m plus 2 k minus 8 m , column 2 cap oppositeofacap sumandcap distributivecap property , row2 column 1 , equals negative k minus 9 m , column 2 cap combineliketerms . . , end table

✓ Got It?

5. Combine like terms. What is a simpler form of each expression?
   1. − 4 j 2 − 7 k + 5 j + j 2 negative 4 , j squared , minus 7 k plus 5 j plus , j squared
   2. − ( 8 a + 3 b ) + 10 ( 2 a − 5 b ) negative open 8 eh plus 3 b close plus 10 open 2 eh minus 5 b close