Distributive Property Review

Distributive Property

100

4 (8 + 3x - 6y)

32 + 12x - 24y

200

70 (19x²-20n³)

1330x²-1400n³

300

45 (45w² - 45w³ + 45w⁴ - 14w⁵)

2025w² - 2025w³ + 2025w⁴ - 630w⁵

400

563 (1,392b - 3862x + 23w - 46y - 14c + 643,463)

783,696b - 2,174,306x + 12,949w - 25,898y - 7,882c + 362,269,669

500

324 (7a²bc³ - 82bc² + 7a²b² - 91d²e⁵)

2268a²bc³ - 26568bc² + 2268a²b² - 29484d²e⁵

Combining Like Terms

100

3a²+7a²

10a²

200

3b²+2a³-b²

2b²+2a³

300

3b³+3b²-7b³

-4b³+3b²

400

b⁴-3b⁴+7a²-a²

-2b²+6a²

500

3a²b+2a²b³-7a²b³

3a²b-5a²b³

Factoring

100

30x - 18y

6(5x - 6y)

200

64y²x + 16yx²

16xy(4y + 1x)

300

45j³b + 42db² - 15d

3(15j³b + 14db² 5d)

400

201 - 3 + 33q

3(67 - 1 + 11q)

500

445a⁴ + 75 - 210 - 655q2

5(89q² + 15 - 42q²)

Real World

100

Romeo was planning a birthday party. He thought that each person would eat 6 hamburgers and 2 cookies. If he invited 12 people including himself. How much of each food will he need?

72 hamburgers + 2 cookies

72b + 2c

200

You have six skittles and 10 sticks of gum. Your friend is going to double the amount of candies, because you helped her. How many candies do you have in total?

12 skittles + 10 sticks of gum

12s + 10g

300

Jimmy ordered 13 red apples (r), 14 green apples (g), 3 cheeseburgers (b), and decided to buy one Pepsi (p). Jimmy then decided that he wanted to give us 4 green apples (g) and 5 red apples (r). What was his total outcome of foods.

8r + 10g + 3b + p

400

Juliet was to host a barbecue and she expected each person to eat 4 Burgers, 2 Sausages, and 2 Drinks. How much does she need of each if Juliet was hosting 18 people?

72 burgers + 36 Sausages + 36 drinks

72b + 36s + 36d

500

Jason decided to place an order at his favorite restaurant. He decided that he wanted to buy 12 small fries (s), 7 burgers (b), 2 cokes (c), 5 large fries (l), and 12 chicken nuggets (n). After analyzing his budget, Jason realized that he did not have enough money. Jason told the waiter that he wanted to take away 4 small fries (s), 1 burger (b), both of his cokes (c), and 3 of his chicken nuggets (n). What was his final order?

8s + 6b + 5l + 9n

🦆 Challenge 😈

100

2(x-17)-3y+7x(14y)-3

-42y²+9x-37

200

17y¹⁷(17)/(17/16)(13y(17(38x⁵)))+3x⁵

17y¹⁷(16)(221y)(494yx⁵)+3x⁵

300

43x³y (b(17)) / 4x + 3yx - 17x³y + 4b - 6a (4b)

43x³yb + 714 / 4x + 3yx - 6a + 4b - 24ab

400

562a⁶p²q⁷ + 4706q³a³ - 200000043786q⁶³

2(281a⁶p²q⁷ + 2353q³a³ - 1000000216393)

500

4³(7x³y⁵(4b+7c))²/3b(4cy⁵(6))⁴b+17-(3/17)y⁶+4y⁶(3²y)(6x)(4³)

(50176x⁶y¹⁰b²)+(12155.0625x⁶c²y¹⁰b¹²)+17-14433.88235yx