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In the expansion of `(x^2 - 1/x^2)^16`, the value of constant term is ______.

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#### Solution

In the expansion of `(x^2 - 1/x^2)^16`, the value of constant term is ** ^{16}C_{8}**.

**Explanation:**

Let T_{r+1} be the constant term in the expansion of `(x^2 - 1/x^2)^16`

∴ T_{r+1} = `""^16"C"_r (x^2)^(16 - r) ((-1)/x^2)^r`

= `""^16"C"_r (x)^(32 - 2r) (-1)^r * 1/x^(2r)`

= `(-1)^r * ""^16"C"_r (x)^(32 - 2r - 2r)`

⇒ `(-1)^r * ""^16"C"_r (x)^(32 - 4r)`

For getting constant term, 32 – 4r = 0

⇒ r = 8

∴ T_{r+1} = `(-1)^8 * ""^16"C"_8 = ""^16"C"_8`

Concept: General and Middle Terms

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