Which expression is equivalent to \((x-1)^7\)?

1) \((x-1)^7\)
2) \(x^7 - 1\)
3) \(x^6 - x\)
4) \(x^7 - 7x^6 + 21x^5 - 35x^4 + 35x^3 - 21x^2 + 7x - 1\)

To find the expression equivalent to (x-1)⁷, we can expand it using the binomial theorem. The binomial theorem states that for any positive integer n, the expansion of (a + b)ⁿ is given by (n choose 0)aⁿ b⁰ + (n choose 1)aⁿ⁻¹ b¹ + ... + (n choose n-1)abⁿ⁻¹ + (n choose n)a⁰ bⁿ.

Using this formula, we can expand (x-1)⁷ as follows:

(7 choose 0)x⁷(-1)⁰ + (7 choose 1)x⁶(-1)¹ + (7 choose 2)x⁵(-1)² + (7 choose 3)x⁴(-1)³ + (7 choose 4)x³(-1)⁴ + (7 choose 5)x²(-1)⁵ + (7 choose 6)x¹(-1)⁶ + (7 choose 7)x⁰(-1)⁷

Simplifying this expression, we get x⁷ - 7x⁶ + 21x⁵ - 35x⁴ + 35x³ - 21x² + 7x - 1.

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Which expression is equivalent to \((x-1)^7\)?1) \((x-1)^7\) 2) \(x^7 - 1\) 3) \(x^6 - x\) 4) \(x^7 - 7x^6 + 21x^5 - 35x^4 + 35x^3 - 21x^2 + 7x - 1\)

Answer :

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Other Questions

Which expression is equivalent to \((x-1)^7\)?

1) \((x-1)^7\)
2) \(x^7 - 1\)
3) \(x^6 - x\)
4) \(x^7 - 7x^6 + 21x^5 - 35x^4 + 35x^3 - 21x^2 + 7x - 1\)