Problem 5 Combining Like Terms

What is the simplified form of each expression?

1. 8 x 2 + 2 x 2 8 , bold italic x squared , plus 2 , bold italic x squared

   8 x 2 + 2 x 2 = ( 8 + 2 ) x 2 Distributive Property   = 10 x 2 Simplify. table with 2 rows and 3 columns , row1 column 1 , 8 , x squared , plus 2 , x squared , column 2 equals open 8 plus 2 close , x squared , column 3 cap distributive cap property , row2 column 1 , , column 2 equals 10 , x squared , column 3 cap simplify. , end table

2. 5 x − 3 − 3 x + 6 y + 4 5 bold italic x minus 3 minus 3 bold italic x plus 6 bold italic y plus 4

   5 x − 3 − 3 x + 6 y + 4 = 5 x + ( − 3 ) + ( − 3 x ) + 6 y + 4 Rewrite as a sum.   = 5 x + ( − 3 x ) + 6 y + ( − 3 ) + 4 Commutative Property   = ( 5 − 3 ) x + 6 y + ( − 3 ) + 4 Distributive Property   = 2 x + 6 y + 1 Simplify. table with 4 rows and 3 columns , row1 column 1 , 5 x minus 3 minus 3 x plus 6 y plus 4 , column 2 equals 5 x plus open negative 3 close plus open negative 3 x close plus 6 y plus 4 , column 3 cap rewrite as a sum. , row2 column 1 , , column 2 equals 5 x plus open negative 3 x close plus 6 y plus open negative 3 close plus 4 , column 3 cap commutative cap property , row3 column 1 , , column 2 equals open 5 minus 3 close x plus 6 y plus open negative 3 close plus 4 , column 3 cap distributive cap property , row4 column 1 , , column 2 equals 2 x plus 6 y plus 1 , column 3 cap simplify. , end table

✓ Got It?

5. What is the simplified form of each expression in parts (a)−(c)?
   1. 3 y − y 3 y minus y
   2. − 7 m n 4 − 5 m n 4 negative 7 m , n to the fourth , minus 5 m , n to the fourth
   3. 7 y 3 z − 6 y z 3 + y 3 z 7 , y cubed , z minus 6 y , z cubed , plus , y cubed , z
   4. Reasoning Can you simplify 8 x 2 − 2 x 4 − 2 x + 2 + x y 8 , x squared , minus 2 , x to the fourth , minus 2 x plus 2 plus x y  further? Explain.

✓ Lesson Check

Do you know HOW?

1. What is the simplified form of each expression? Use the Distributive Property.
   1. (j + 2)7
   2. − 8 ( x − 3 ) negative 8 open x minus 3 close
   3. − ( 4 − c ) negative open 4 minus c close
   4. − ( 11 + 2 b ) negative open 11 plus 2 b close

Rewrite each expression as a sum.

2. − 8 x 2 + 3 x y − 9 x − 3 negative 8 , x squared , plus 3 x y minus 9 x minus 3
3. 2 a b − 5 a b 2 − 9 a 2 b 2 eh b minus 5 eh , b squared , minus 9 , eh squared , b

Tell whether the terms are like terms.

4. 3a and − 5 negative 5 a
5. 2 x y 2 2 x , y squared  and − x 2 y negative , x squared , y

Do you UNDERSTAND?

6. Vocabulary Does each equation demonstrate the Distributive Property? Explain.
   1. − 2 ( x + 1 ) = − 2 x − 2 negative 2 open x plus 1 close equals negative 2 x minus 2
   2. ( s − 4 ) 8 = 8 ( s − 4 ) open s minus 4 close 8 equals 8 open s minus 4 close
   3. 5 n − 45 = 5 ( n − 9 ) 5 n minus 45 equals 5 open n minus 9 close
   4. 8 + ( t + 6 ) = ( 8 + t ) + 6 8 plus open t plus 6 close equals open 8 plus t close plus 6
7. Mental Math How can you express 499 to find the product 499 × 5 499 times 5  using mental math? Explain.
8. Reasoning Is each expression in simplified form? Justify your answer.
   1. 4 x y 3 + 5 x 3 y 4 x , y cubed , plus 5 , x cubed , y
   2. − ( y − 1 ) negative open y minus 1 close
   3. 5 x 2 + 12 x y − 3 y x 5 , x squared , plus 12 x y minus 3 y x