Distributive Law & Binomial Expansion

Collect Like Terms

100

3r + 7r + 3r – 10 = 

13r - 10

200

-12 + 4 – 10t + 6t =

-8 – 4t

300

2b + 7b² - 5b² + 14 – 4 =

2b² + 2b + 10

400

5 + 5a² - 2a² - 6a + 3a =

5 + 3a² - 3a

500

-12² + 4 – 10t³ + 6t³ - 3t = 

148 - 4t³ - 3t

Distributive Law

100

5(x + 2)

5x + 10

200

10(c – 5)

10c - 50 

300

4(x + 3y)

4x + 12y

400

6x²(2x + 10x²) = 

12x³ + 60x⁴

500

-2x(x – 8y² + 3 - 10xy) = 

12x² + 16xy² - 6x + 20x²y

Binomial Expansion

100

(x + 2)(x + 3) =

x² + 3x + 2x + 6

= x² + 5x + 6

200

(b² + 4) (b + 2) =

b³ + 2b² + 4b + 8

300

(r + 6)(r – 2) = 

= r² - 2r + 6r – 12

= r²  + 4r – 12 

400

(n² - 1)(n - 4) =

n³ - 4n - 1n + 4

= n³ - 5n + 4 

500

(5c - 2r + 4)(3 - r)

= 15c - 5cr -6r + 2r² + 12 - 4r

= 15c - 5cr -10r + 2r² + 12

Solving Equations

100

e + 20 = 24

e = 4

200

5w = 30

w = 6

300

f ÷ 6 = 10

f = 60

400

3m + 7 = 19

m = 4

500

5t + 10 = -15

t = -5