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What is the number of terms in the expansion of {(2x – 3y)2 (2x + 3y)2}2?

What is the number of terms in the expansion of {(2x – 3y)2 (2x + 3y)2}2? Correct Answer 5

Concept:

In the binomial expansion of (a + b)n there are n + 1 terms.

Calculation:

⇒ {(2x – 3y)2 (2x + 3y)2}2 = {(2x -3y)× (2x + 3y) × (2x – 3y) × (2x + 3y)}2

As we know that, (a - b) × (a + b) = a2 – b2

⇒ {(2x – 3y)2 (2x + 3y)2}2 = {(4x2 – 9y2)2}2 = (4x2 – 9y2)4

As we know that, in the binomial expansion of (a + b)n there are n + 1 terms.

Here, a = 4x2, b = - 9y2 and n = 4.

Hence, there are 5 terms in the expansion of {(2x – 3y)2 (2x + 3y)2}2.

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