High School

What is the result of adding \((7x^8 + 3x^7 + 5x^6 + 4)\) and \((7x^8 + 5x^7 - 7x^6 + 2)\)?

1) \(9x^8 + 9x^7 + 9x^6 + 10\)
2) \(14x^{16} + 8x^{14} - 2x^{12} + 6\)
3) \(20x^{42} + 6\)
4) \(14x^8 + 8x^7 - 2x^6 + 6\)

Answer :

The sum of the polynomials (7x⁸+3x⁷+5x⁶+4) and (7x⁸+5x⁷-7x⁶+2) is 14x⁸+8x⁷-2x⁶+6(4), found by combining like terms and adding their respective coefficients.

The result of adding the two given polynomials (7x⁸+3x⁷+5x⁶+4) and (7x⁸+5x⁷-7x⁶+2) is done by combining like terms. To do this, we simply find the terms with the same exponent and add their coefficients:

  • Add the coefficients of x⁸ terms: 7 + 7 = 14, so we get 14x⁸.
  • Add the coefficients of x⁷ terms: 3 + 5 = 8, resulting in 8x⁷.
  • Add the coefficients of x⁶ terms: 5 - 7 = -2, resulting in -2x⁶.
  • Add the constant terms: 4 + 2 = 6.

Putting it all together, we obtain the answer 14x⁸+8x⁷-2x⁶+6.

Other Questions