Algebraic Expressions

Vocab

100

Identify the variables in the following algebraic expression: 7x + 2y - 2.3 + 9a

x, y, and a

200

Identify the coefficients in the following algebraic expression: 9p + 2 + q - 1

9 and 1

300

Identify the constant term in the following algebraic expression: 2d + 9.2 + 12t

9.2

400

How do you factor?

Find the GCF of the terms and divide every term by the GCF.  

500

After the following algebraic expression is simplified, how many terms will it have:

9b + 7b + 4 - 16b - d + 4c - 12 + c

3 terms

Writing Expressions

100

Write an algebraic expression to model the following situation: Total cost for m muffins and d donuts, if muffins cost $3.20 each and donuts cost $2.95 each.

3.2m + 2.95d (or 2.95d + 3.2m)

200

Jim is j years old. Alex is 4 years younger than Jim. Write an expression to indicate how old is Alex in terms of j?

j - 4

300

Write an algebraic expression to model the following situation: Josh has $45 in his bank account, and he buys x candy bars for $1.50 each.

45 - 1.5x

400

Write an algebraic expression in simplest form to model the following situation: Everett and Melinda were putting their saved money together to buy a bike. Everett had -12m + 6 dollars and Melinda had 9(2 + 5m) dollars. How much do they have total?

(-12m + 6) + 9(2 + 5m)

(-12m + 6) + 18 + 45m

33m + 24

500

Write an algebraic expression in simplest form to model the following situation: The distance between Lily and Paul, if in an hour Lily ran a distance of 14m + 16 miles and Paul ran a distance of 5m + 30 miles

(14m + 16) - (5m + 30)

(14m + 16) + (-5m - 30)

9m - 14

Translate

100

Write an algebraic expression to model the following situation: 7 more than one-half of p

0.5p+7      OR

p/2+7        OR

1/2P+7

200

Jim is j years old. Alex is 4 years younger than Jim. How old is Alex in terms of j?

j-4

300

Write an algebraic expression to model the following situation: 17 less than the quotient of k and 4

k/4 - 17

400

Write an algebraic expression to model the following situation: 6 less than the product of 8 and k

8k - 6

500

Write an algebraic expression to model the following situation: The product of k minus 2 and 3

3(k-2)

Distribution and Factoring

100

Simplify the following expression:

5(x−4)

5x - 20

200

Simplify the following expression:

−3(2w−7)

-6w+21

300

Factor completely.

6h - 20

2(3h-10)

400

Factor completely.

-24ab - 18a

-6a(4b+3)

500

Simplify the following expression:

−5(−3x−7y+4)

15x+35y−20

Simplify

100

Simplify the following expression: v + v + 5 - 2 + 3v

5v + 3

200

Simplify the following expression: 4k + 3j + 6 + k + 8j

5k+11j+6

300

Simplify the following expression: 4(d-3f)+14f

4d+2f

400

Simplify the following expression: 3 + 8p + 3r - 4p + 6p + 1 - r

10p+2r+4

500

Simplify the following expression:

17 + 15x - 10 - 12x - 6(z + x)

-3x + 7 - 6z

Simplify #2

100

(2v + 7) + (13v - 5)

15v + 2

200

(16x - 3) + (-10x - 8)

6x - 11

300

(9y + 14) - (4y - 8)

5y + 22

400

(6 - 3b) - (b + 16)

-4b - 10

500

(15 + 7x - 10y) - (y + 4x - 5)

-11y + 3x + 20

Simplify #3

100

Add the linear expressions:

(2x−7)+(3x+9)

5x+2

200

Add the linear expressions:

(c−2)+(3c+2)

2c

300

Simplify:

(6w+6) − 3(−w−3)

9w+15

400

Subtract the linear expressions:

3(5k−1)−(−6k+2)

21k-5

500

Subtract the linear expressions:

(4r−7)−3(3−r)

7r-16