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.

(m + 2)4 = m4 + m3 + m2 + m +

Answer 1

m^4 +8m^3 +24m^2 +32m +16

Explanation:

To simplify the expression, you must evaluate the constant coefficients.

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(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)

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

= m^4 +8m^3 +24m^2 +32m +16