Algbrea 2 Math

Question

(3a+5)^3= 

 

Multiply

Answer 1

 Pascal's Triangle, find n = 3

 

(x+y)ⁿ

 

n = 0    1

n = 1   1 1

n = 2  1 2 1

n = 3 1 3 3 1

 

x = 3a

y = 5

n = 3

 

1(3a)³(5)⁰ + 3(3a)²(5)¹ + 3(3a)¹(5)² + 1(3a)⁰(5)³

 

27a3 + 3(9a2)(5) + 9a(25) + 125

 

27a³ +135a² + 225a + 125


Or brute force:

 

(3a + 5)(3a + 5) (3a + 5)

 

First two using FOIL:

(9a² + 30a + 25)(3a + 5)

 

Distribute:

(27a³ + 90a² + 75a) + (45a² + 150a + 125)

 

27a³ + 135a² + 225a + 125