Answered

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What is the difference of the polynomials?

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

A. [tex]\(7x^2 + 3y^2 - 4x\)[/tex]

B. [tex]\(7x^2 - 3y^2 - 4x\)[/tex]

C. [tex]\(7x^2 - 25y^2 - 22x\)[/tex]

D. [tex]\(17x^2 - 25y^2 - 22x\)[/tex]

Sagot :

GinnyAnswer
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 each term.

1. Subtract the [tex]\(x^2\)[/tex] terms:

[tex]\[ 12x^2 - 5x^2 = (12 - 5)x^2 = 7x^2 \][/tex]

2. Subtract the [tex]\(y^2\)[/tex] terms:

[tex]\[ -11y^2 - (-14y^2) = -11y^2 + 14y^2 = (14 - 11)y^2 = 3y^2 \][/tex]

3. Subtract the [tex]\(x\)[/tex] terms:

[tex]\[ -13x - (-9x) = -13x + 9x = (-13 + 9)x = -4x \][/tex]

By combining these results, the resulting polynomial is:

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

Thus, the correct answer is [tex]\(7x^2 + 3y^2 - 4x\)[/tex].
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