contestada

Subtract the following polynomials, then place the answer in the pro
descending powers of x.
(-6.7x2 + 2.3x y + 5.2) - (-14.9x2 - 3.5x y+ 7.1)
1|2|3|4|5|6|7|8|9|0|0|| | . |-| + " ""

Respuesta :

Edufirst

Answer:

  • [tex]8x^2+5.8xy-1.9[/tex]

Explanation:

The polynomial subtraction is:

  • [tex](-6.7x^2+2.3xy + 5.2)-(-14.9x^2-3.5xy+7.1)[/tex]

The ruls to add or subtract polynomials is to add or subtract like terms.

LIke terms are the terms with the same variables each raised to the same power. So, the like terrms for those two polynomilas are:

  • -6.7x² and -14.9x²,
  • +2.3xy and -3.5xy,
  • 5.2 and 7.1

The next step is to use the distributive property: you must distribute the subraction symbol before the parenthesis through every term inside the parenthesis. For this, remember the rule of the signs:

  • When you multiply the negative sign before the parenthesis, the sign of each term inside the parenthesis will be changed (negative times positive = negative, negative times negative = positive)

So, the result is:

[tex](-6.7x^2+2.3xy + 5.2)-(-14.9x^2-3.5xy+7.1)=-6.7x^2+2.3xy + 5.2+14.9x^2+3.5xy-7.1\\ \\ -6.7x^2+14.9x^2+2.3xy+3.5xy+5.2-7.1\\ \\8.2x^2+5.8xy-1.9[/tex]

And that is ordered in descending powers of x (x² has order 2, xy has order 1 on each variable, and the constant terms have order 0).