Expand the Expression Using the Binomial Theorem $$( 2 x + y ) ^ { 6 }$$

question 41

Multiple Choice

Expand the expression using the Binomial Theorem.
- $$( 2 x + y ) ^ { 6 }$$

• A) \(64 x ^ { 6 } + 192 x ^ { 5 } y + 480 x ^ { 4 } y ^ { 2 } + 960 x ^ { 3 } y ^ { 3 } + 1440 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }\)
• B) \(64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 60 x ^ { 2 } y ^ { 4 } + 12 x y ^ { 5 } + y ^ { 6 }\)
• C) \(64 x ^ { 6 } + 192 x ^ { 5 } y + 240 x ^ { 4 } y ^ { 2 } + 160 x ^ { 3 } y ^ { 3 } + 240 x ^ { 2 } y ^ { 4 } + 192 x y ^ { 5 } + 64 y ^ { 6 }\)
• D) \(2 x ^ { 6 } + 12 x ^ { 5 } y + 30 x ^ { 4 } y ^ { 2 } + 40 x ^ { 3 } y ^ { 3 } + 12 x y ^ { 5 } + y ^ { 6 }\)

---

Definitions:

Normal Curve

A symmetrical, bell-shaped curve representing the distribution of a set of data where most measurements are close to the average.

Symmetry

The property of being made up of exactly similar parts facing each other or around an axis; often evaluated in statistical data sets.

Normal Distribution

A symmetrical, bell-shaped distribution of data wherein most observations cluster around the central peak and probabilities for values taper off equally in both directions.

Mean

The arithmetic average of a set of values, calculated by summing all the values and then dividing by the number of values.