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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]



Answer :

GinnyAnswer
Let's determine the difference of the given polynomials step-by-step.

We are given two polynomials:
[tex]\[ P_1 = 12x^2 - 11y^2 - 13x \][/tex]
[tex]\[ P_2 = 5x^2 - 14y^2 - 9x \][/tex]

We need to find the difference [tex]\( P_1 - P_2 \)[/tex].

1. Subtract the coefficients of [tex]\( x^2 \)[/tex]:
[tex]\[ 12x^2 - 5x^2 = 7x^2 \][/tex]

2. Subtract the coefficients of [tex]\( y^2 \)[/tex]:
[tex]\[ -11y^2 - (-14y^2) = -11y^2 + 14y^2 = 3y^2 \][/tex]

3. Subtract the coefficients of [tex]\( x \)[/tex]:
[tex]\[ -13x - (-9x) = -13x + 9x = -4x \][/tex]

Therefore, the difference of the polynomials is:
[tex]\[ 7x^2 + 3y^2 - 4x \][/tex]

So the correct answer is:
[tex]\[ 7x^2 + 3y^2 - 4x \][/tex]

Given the options, the correct one is:
[tex]\[ 7x^2 + 3y^2 - 4x \][/tex]

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