Question

Which of the following is equivalent to the expression (m + 3)4? 4C0m430 + 4C1m331 + 4C2m232 + 4C3m133 + 4C4m034 4C1m430 + 4C2m331 + 4C3m232 + 4C4m133 + 4C5m034 4C0m434 + 4C1m333 + 4C2m232 + 4C3m131 + 4C4m030 4C4m434 + 4C3m433 + 4C2m432 + 4C1m431 + 4C0m430 A is the right answer)4C0m430 + 4C1m331 + 4C2m232 + 4C3m133 + 4C4m034
4C0m430 + 4C1m331 + 4C2m232 + 4C3m133 + 4C4m034 is the right answer

Answer 1

Answer:

4C0(m⁴)(3⁰) + 4C1(m³)(3¹) + 4C2(m²)(3²) + 4C3(m¹)(3³) + 4C4(m⁰3⁴)

Step-by-step explanation:

Using Pascal's triangle, going to the 4th line down, the coefficients are 1, 4, 6, 4 and 1.  This is the same as 4C0, 4C1, 4C2, 4C3, and 4C4.

In these expansions, the exponent for the first term of the binomial will start at 4 and decrease, while the exponent for the second term of the binomial will start at 0 and increase.

This gives us

4C0(m⁴)(3⁰) + 4C1(m³)(3¹) + 4C2(m²)(3²) + 4C3(m¹)(3³) + 4C4(m⁰3⁴).

Answer 2

The correct answer is 4C0m430 + 4C1m331 + 4C2m232 + 4C3m133 + 4C4m034