High School

Which expression is equivalent to \((6x^8 + 7x^7 - 3x^6 + 1) - (3x^8 - 4x^7 + 7x^6 - 6)\)?

A. \(3x^8 + 3x^7 + 4x^6 - 5\)

B. \(9x^5 + 3x^7 + 4x^6 - 5\)

C. \(9x^5 + 3x^7 + 4x^6 + 7\)

D. \(3x^5 + 11x^7 - 10x^6 + 7\)

Answer :

The correct option is (A) which is "3x⁸+3x⁷+4x⁶-5". The equivalent expression to the given polynomial subtraction (6x^8+7x^7-3x^6+1)-(3x^8-4x^7+7x^6-6) is 3x^8 + 11x^7 - 10x^6 + 7.

The expression equivalent to (6x8+7x7-3x6+1)-(3x8-4x7+7x6-6) is found by performing the subtraction term-by-term. This involves subtracting the coefficients of the like powers of x. Here is the step-by-step process:

  1. Subtract the coefficients of x8: 6x8 - 3x8 = 3x8.
  2. Subtract the coefficients of x7: 7x7 - (-4x7) = 7x7 + 4x7 = 11x7.
  3. Subtract the coefficients of x6: -3x6 - 7x6 = -10x6.
  4. The constant terms: 1 - (-6) = 1 + 6 = 7.

The equivalent expression is 3x8 + 11x7 - 10x6 + 7. Therefore, the correct option is (A) which is "3x⁸+3x⁷+4x⁶-5".

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