Write the Binomial Expansion of the Expression $$\left( 2 x ^ { 2 } - y \right) ^ { 5 }$$

question 34

Multiple Choice

Write the binomial expansion of the expression.
- $$\left( 2 x ^ { 2 } - y \right) ^ { 5 }$$

• A) \(- 32 x^{ 10} + 80 x ^ { 8 } y - 80 x ^ { 6 } y ^ { 2 } + 40 x ^ { 4 } y ^ { 3 } - 10 x ^ { 2 } y ^ { 4 } + y ^ { 5 }\)
• B) \(32 x ^ { 10 } - 80 x ^ { 8 } y + 80 x ^ { 6 } y ^ { 2 } - 40 x ^ { 4 } y ^ { 3 } + 10 x ^ { 2 } y ^ { 4 } - y ^ { 5 }\)
• C) \(32 x ^ { 10 } - 80 x ^ { 8 } y - 80 x ^ { 6 } y ^ { 2 } - 40 x ^ { 4 } y ^ { 3 } - 10 x ^ { 2 } y ^ { 4 } - y ^ { 5 }\)
• D) \(32 x ^ { 10 } + 80 x ^ { 8 } y + 80 x ^ { 6 } y ^ { 2 } + 40 x ^ { 4 } y ^ { 3 } + 10 x ^ { 2 } y ^ { 4 } + y ^ { 5 }\)

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Definitions:

Infinite Slope

This represents a vertical line in a graph, indicating a situation where a small change in one variable causes an infinitely large change in another variable.

Dome-Shaped

A physical description of a structure or object that has a rounded, upward-curving shape reminiscent of a dome.

Inversely Related

A relationship between two variables where one increases as the other decreases, or vice versa.

Upward-Sloping

Characteristic of a line or curve that rises as it moves from left to right, used to describe certain types of supply curves.