Question

Write 5 examples of the form (a + b + c)² and expand them using the formula.

Answer 1

Answer:

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Step-by-step explanation:

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

Case 1 :

a = 1  , b = 2 , c = 3

(1 + 2 + 3)² = 1² + 2² + 3² + 2(1)(2) + 2(2)(3) + 2(1)(3)

=> 6² = 1 + 4 + 9 + 4 + 12 + 6

=> 36 = 36

Case 2:

a = 1  , b = 2 , c = 4

(1 + 2 + 4)² = 1² + 2² + 4² + 2(1)(2) + 2(2)(4) + 2(1)(4)

=> 7² = 1 + 4 + 16 + 4 + 16 + 8

=> 49 = 49

Case 3:

a = 1  , b = 4 , c = 3

(1 + 4 + 3)² = 1² + 4² + 3² + 2(1)(4) + 2(4)(3) + 2(1)(3)

=> 8² = 1 + 16 + 9 + 8 + 24 + 6

=> 64 = 64

Case 4 :

a = 2  , b = 2 , c = 3

(2 + 2 + 3)² = 2² + 2² + 3² + 2(2)(2) + 2(2)(3) + 2(2)(3)

=> 7² = 4 + 4 + 9 + 8 + 12 + 12

=> 49 = 49

Case 5:

a = 2  , b = 4 , c = 3

(2+ 4 + 3)² = 2² + 4² + 3² + 2(2)(4) + 2(4)(3) + 2(2)(3)

=> 9² = 4 + 16 + 9 + 16 + 24 + 12

=> 81 = 81