Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

What is the difference of the polynomials?

[tex]\[
\left(12 x^2 - 11 y^2 - 13 x \right) - \left(5 x^2 - 14 y^2 - 9 x \right)
\][/tex]

A. [tex]7 x^2 + 3 y^2 - 4 x[/tex]
B. [tex]7 x^2 - 3 y^2 - 4 x[/tex]
C. [tex]7 x^2 - 25 y^2 - 22 x[/tex]
D. [tex]17 x^2 - 25 y^2 - 22 x[/tex]

Sagot :

To find the difference of the polynomials [tex]\((12x^2 - 11y^2 - 13x) - (5x^2 - 14y^2 - 9x)\)[/tex], we need to subtract the corresponding coefficients of the like terms in each polynomial.

1. Identify like terms in the polynomials:
- The terms involving [tex]\(x^2\)[/tex]: [tex]\(12x^2\)[/tex] and [tex]\(5x^2\)[/tex]
- The terms involving [tex]\(y^2\)[/tex]: [tex]\(-11y^2\)[/tex] and [tex]\(-14y^2\)[/tex]
- The terms involving [tex]\(x\)[/tex]: [tex]\(-13x\)[/tex] and [tex]\(-9x\)[/tex]

2. Subtract the coefficients of the like terms:
- For [tex]\(x^2\)[/tex]: [tex]\(12x^2 - 5x^2 = 7x^2\)[/tex]
- For [tex]\(y^2\)[/tex]: [tex]\(-11y^2 - (-14y^2) = -11y^2 + 14y^2 = 3y^2\)[/tex]
- For [tex]\(x\)[/tex]: [tex]\(-13x - (-9x) = -13x + 9x = -4x\)[/tex]

3. Combine the results:
- The difference of the polynomials is: [tex]\(7x^2 + 3y^2 - 4x\)[/tex]

So, the resulting polynomial after subtracting the given polynomials is:

[tex]\[ 7x^2 + 3y^2 - 4x \][/tex]

Therefore, the correct answer is:

[tex]\[ \boxed{7x^2 + 3y^2 - 4x} \][/tex]