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Simplify:

[tex]\[ \frac{9x^6 y - 21x^2 y^2}{3x^2} \][/tex]

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

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

C. [tex]\( 3x^6 y - 7x^2 y^2 \)[/tex]

Answer :

Sure! Let's simplify the given expression step-by-step:

We need to simplify the expression:
[tex]\[
\frac{9x^6y - 21x^2y^2}{3x^2}
\][/tex]

1. Distribute the division across the terms in the numerator:
[tex]\[
\frac{9x^6y}{3x^2} - \frac{21x^2y^2}{3x^2}
\][/tex]

2. Simplify each term separately:

- For the first term [tex]\(\frac{9x^6y}{3x^2}\)[/tex]:
- Divide the coefficients: [tex]\( \frac{9}{3} = 3 \)[/tex].
- For the [tex]\(x\)[/tex] terms: [tex]\( x^6 \div x^2 = x^{6-2} = x^4 \)[/tex].
- The [tex]\(y\)[/tex] term remains as [tex]\(y\)[/tex].

So, [tex]\(\frac{9x^6y}{3x^2} = 3x^4y\)[/tex].

- For the second term [tex]\(\frac{21x^2y^2}{3x^2}\)[/tex]:
- Divide the coefficients: [tex]\( \frac{21}{3} = 7 \)[/tex].
- For the [tex]\(x\)[/tex] terms: [tex]\( x^2 \div x^2 = x^{2-2} = x^0 = 1 \)[/tex] (since anything raised to the power of 0 is 1).
- The [tex]\(y^2\)[/tex] term remains as [tex]\(y^2\)[/tex].

So, [tex]\(\frac{21x^2y^2}{3x^2} = 7y^2\)[/tex].

3. Combine the simplified terms:
[tex]\[
3x^4y - 7y^2
\][/tex]

Thus, the simplified form of the expression is:
[tex]\[
3x^4y - 7y^2
\][/tex]

So, the correct answer is:
[tex]\[
\boxed{3x^4y - 7y^2}
\][/tex]

This matches option B from the provided choices.

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