Question

The terms of the binomial expansion are written below using the patterns. (m + 2)4 = (1)(m4)(20) + (4)(m3)(21) + (6)(m2)(22) + (4)(m1)(23) + (1)(m0)(24) Simplify each term to complete the expansion.

Answer 1

Answer:

$(m + 2)^4 = m^4+ 8 m^3 + 24 m^2 + 32 m + 16$

Step-by-step explanation:

$(m + 2)^4 = (1)(m^4)(2^0) + (4)(m^3)(2^1) + (6)(m^2)(2^2) + (4)(m^1)(2^3) + (1)(m^0)(2^4)$

2^0 is 1 also m^0 is 1

2^2= 4, 2^3= 8 , 2^4= 16

$(m + 2)^4 = (1)(m^4)(1)+ (4)(m^3)(2) + (6)(m^2)(4) + (4)(m^1)(8) + (1)(1)(16)$

$(m + 2)^4 = m^4+ 8 m^3 + 24 m^2 + 32 m + 16$