The Distributive Property
Simplifying Algebraic Expression
Adding Linear Expressions
Subtracting Linear Expressions
Apply It!
100
Use the Distributive Property to expand:
3(–2x + 2)
-6x + 6
100
Identify the terms and like terms
6n - 3n - 5m + 12 + 9m2 - 4
terms: 6n, -3n, -5m, 12, 9m2, - 4
like terms: 6n, -3n, & 12, 4
100
Add the linear expressions:
(5x - 4) + (9x + 5)
14x + 1
100
Subtract the linear expressions:
(-5x + 4) - (-3x + 2)
-2x + 2
100
Darnell began with $85 in his savings account. Each week he saves an additional $15. The expression 15w+85 represents how much Darnell has saved after w weeks. Missy saves the same amount as Darnell each week but began with $30 more in her account. If they opened their accounts at the same time, write an expression that represents the total amount saved by Darnell and Missy after w weeks?
30w + 200
200
Use the Distributive Property to expand:
–2(x + 1)
-2x - 2
200
Simplify the expression
-8a - 3a + 15b + 9 + 6
-11a + 15b + 15
200
Add the linear expressions:
(-x + 4) + (-2x - 5)
-3x - 1
200
Subtract the linear expressions:
(11x + 3) - (-4x + 12)
15x - 9
200
You earn (4x + 12) points after completing x levels of a video game and then lose (2x − 5) points. Write an expression that represents the total number of points you have now.
2x + 7
300
Use the Distributive Property to expand:
–1/4(–20m + 36)
5m - 9
300
Simplify the expression
4x - 3x + 2x + 12 - 19
3x -7
300
Add the linear expressions:
(x - 1) + (-2x + 7)
-x + 6
300
Subtract the linear expressions:
(x - 6) - (13x - 12)
-12x + 6
300
You start a new job. After w weeks, you have (10w + 120) dollars in your savings account and (45w + 25) dollars in your checking account.
Write an expression that represents the total in both accounts.
55w + 145
400
Use the Distributive Property to expand:
–2(7.5g - 9.5)
-15g + 19
400
Simplify the expression
2c - 3d - 5c + 4d + 8
-3c + d + 8
400
Add the linear expressions:
(3x - 4) + 3(-2x - 9)
3x - 31
400
Subtract the linear expressions:
(-9x - 9) - 6(2x + 1)
-21x - 15
400
The original price of a cowboy hat is d dollars. You use a coupon and buy the hat for (d − 2) dollars. You decorate the hat and sell it for (2d − 4) dollars. Write an expression that represents your earnings from buying and selling the hat. Interpret the expression.
d − 2
500
Use the Distributive Property to expand:
-12(-3x - 3) - 1/3(27x -12)
27x + 40
500
Simplify the expression
12m - 19 x - 3m + 19x + 12 - 18
9m - 6
500
Add the linear expressions:
-1/3(9x + 3) + 1/4(-12x + 8)
-6x + 1
500
Subtract the linear expressions:
(8 - x) - 1/5(-10 + 15x)
-4x + 10
500
The expression 17n + 11 represents the perimeter (in feet) of the triangle. Write an expression that represents the measure of the third side.
8n or 8n + 0