Distributive property:

For every real number a, b, and c: a(b + c) = ab + ac and (b+ c)a = ab + ac or a(b - c) = ab - ac and (b - c)a = ab - ac. 

 

Ex. Use distributive property to simplify.

A.) 52(2 + 100) = ?

1st: (52)(2) + (52)(100)

2nd: (104) + (5200)

answer: 5,304

 

B.) 12(7 + 19) = ?

1st: (12)(7) + (12)(19)

2nd: (84) + (228)

answer: 312

 

 

Term: a number, variable, or the product of numbers and variables.

 

Ex. How many terms are in this expression?

A.) 6a² - 5ab +12b -10

 

answer 4

 

 Ex. Simplify (these equations contain terms)  3(6x + 3)

1st: (3)(6x) + (3)(3)

answer: (18x) + (9)

 

 

Coefficient: a number in front of a variable.

 

ex. Name the coefficient.     6x

answer: 6 is the coeffiecent

 

 

Constant: number by itself.

 

ex. This is a constant

A.) 8

answer: 8 is a constant

 

 

 

Like Terms: have same variables and the same exponants.  You may add or subtract like terms.

 

ex. Add or subtract these like terms.

A.) 4x + 8x

answer: 12x

 

B.) -8k + 6k

answer: -2k

 

ex.  Write an algebraic  expression!

A.) 3 times the quantity of x plus 211

1st: 3(x + 211)

2nd: (3)(x) + (3)(211)

answer: 3x + 633

 

 

 

Practice the Distributive Property (answers are at bottom)

 

 

 

1.) 51(11 + 9) = ?

 

2.) -2x(1 + 3) = ?

 

3.) 12(7 - .0025) = ?

 

4.) 21(1000 + 20) = ?

 

 

5.) -11(n - 8) = ?

 

6.) 8(300 + 4) = ?

 

 

How many terms are in these expressions?

 

 

7.) -x + y +3x -1

 

8.) 12(7m - m)

 

9.) 789w

 

 

10.) 12x + 2x - 78x

 

 

 

 

 

Answers

 

1.) 1020

 

2.) -8x

 

3.) .03

 

4.) 21420

 

5.) -11n + 88

 

6.) 2432

 

7.) 3

 

8.) 1

 

9.) 1

 

10.) 1