Simplify:${ \frac{-12xy}{7y^4} \cdot \frac{21x 5y 2}{4y} }$ { \frac{[?]x^{[]}}{y^{[]}} \}

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Introduction

Simplifying algebraic expressions is a crucial skill in mathematics, and it involves combining like terms, canceling out common factors, and rearranging the expression to make it easier to understand and work with. In this article, we will simplify the given algebraic expression, which involves multiplying two fractions and then simplifying the resulting expression.

The Given Algebraic Expression

The given algebraic expression is:

βˆ’12xy7y4β‹…21x5y24y\frac{-12xy}{7y^4} \cdot \frac{21x^5y^2}{4y}

This expression involves multiplying two fractions, and our goal is to simplify it and express it in a more manageable form.

Step 1: Multiply the Numerators and Denominators

To simplify the expression, we need to multiply the numerators and denominators separately. The numerator of the first fraction is -12xy, and the numerator of the second fraction is 21x5y2. Multiplying these two numerators, we get:

βˆ’12xyβ‹…21x5y2=βˆ’252x6y3-12xy \cdot 21x^5y^2 = -252x^6y^3

Similarly, the denominator of the first fraction is 7y^4, and the denominator of the second fraction is 4y. Multiplying these two denominators, we get:

7y4β‹…4y=28y57y^4 \cdot 4y = 28y^5

Step 2: Write the Expression as a Single Fraction

Now that we have multiplied the numerators and denominators, we can write the expression as a single fraction:

βˆ’252x6y328y5\frac{-252x^6y^3}{28y^5}

Step 3: Simplify the Fraction

To simplify the fraction, we need to cancel out any common factors between the numerator and denominator. In this case, we can cancel out a factor of 28 from the numerator and denominator:

βˆ’252x6y328y5=βˆ’9x6y3y5\frac{-252x^6y^3}{28y^5} = \frac{-9x^6y^3}{y^5}

Step 4: Simplify the Expression Further

We can simplify the expression further by canceling out a factor of y^3 from the numerator and denominator:

βˆ’9x6y3y5=βˆ’9x6y2\frac{-9x^6y^3}{y^5} = \frac{-9x^6}{y^2}

Conclusion

In this article, we simplified the given algebraic expression by multiplying the numerators and denominators, writing the expression as a single fraction, and canceling out common factors. The final simplified expression is:

βˆ’9x6y2\frac{-9x^6}{y^2}

This expression is much simpler and easier to work with than the original expression.

Final Answer

The final answer is βˆ’9x6y2\boxed{\frac{-9x^6}{y^2}}.

Discussion

Simplifying algebraic expressions is an important skill in mathematics, and it involves combining like terms, canceling out common factors, and rearranging the expression to make it easier to understand and work with. In this article, we simplified the given algebraic expression by multiplying the numerators and denominators, writing the expression as a single fraction, and canceling out common factors. The final simplified expression is βˆ’9x6y2\frac{-9x^6}{y^2}.

Related Topics

  • Simplifying algebraic expressions
  • Canceling out common factors
  • Rearranging expressions
  • Multiplying fractions

References

Further Reading

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Introduction

In our previous article, we simplified the given algebraic expression by multiplying the numerators and denominators, writing the expression as a single fraction, and canceling out common factors. In this article, we will answer some frequently asked questions related to simplifying algebraic expressions.

Q&A

Q: What is the first step in simplifying an algebraic expression?

A: The first step in simplifying an algebraic expression is to combine like terms. This involves adding or subtracting terms that have the same variable and exponent.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to cancel out any common factors between the numerator and denominator. This can be done by dividing both the numerator and denominator by the greatest common factor (GCF).

Q: What is the difference between simplifying and factoring?

A: Simplifying an algebraic expression involves combining like terms, canceling out common factors, and rearranging the expression to make it easier to understand and work with. Factoring an algebraic expression involves expressing it as a product of simpler expressions.

Q: Can I simplify an algebraic expression by canceling out a factor that is not common to both the numerator and denominator?

A: No, you cannot simplify an algebraic expression by canceling out a factor that is not common to both the numerator and denominator. This would result in an incorrect expression.

Q: How do I know if an algebraic expression is already simplified?

A: An algebraic expression is already simplified if there are no like terms that can be combined, and there are no common factors that can be canceled out.

Q: Can I simplify an algebraic expression by rearranging the terms?

A: Yes, you can simplify an algebraic expression by rearranging the terms. However, this should be done carefully to ensure that the expression is still equivalent to the original expression.

Q: What is the importance of simplifying algebraic expressions?

A: Simplifying algebraic expressions is important because it makes them easier to understand and work with. It also helps to avoid errors and makes it easier to solve equations and inequalities.

Example Questions

Q: Simplify the expression 12x2y36x2y2\frac{12x^2y^3}{6x^2y^2}.

A: To simplify this expression, we need to cancel out the common factors between the numerator and denominator. The greatest common factor (GCF) of 12 and 6 is 6, and the GCF of x2x^2 and x2x^2 is x2x^2. The GCF of y3y^3 and y2y^2 is y2y^2. Therefore, we can cancel out the common factors as follows:

12x2y36x2y2=2xy1\frac{12x^2y^3}{6x^2y^2} = \frac{2xy}{1}

Q: Simplify the expression 18x3y46x2y2\frac{18x^3y^4}{6x^2y^2}.

A: To simplify this expression, we need to cancel out the common factors between the numerator and denominator. The greatest common factor (GCF) of 18 and 6 is 6, and the GCF of x3x^3 and x2x^2 is x2x^2. The GCF of y4y^4 and y2y^2 is y2y^2. Therefore, we can cancel out the common factors as follows:

18x3y46x2y2=3xy21\frac{18x^3y^4}{6x^2y^2} = \frac{3xy^2}{1}

Conclusion

In this article, we answered some frequently asked questions related to simplifying algebraic expressions. We also provided examples of how to simplify expressions by canceling out common factors and rearranging terms. Simplifying algebraic expressions is an important skill in mathematics, and it involves combining like terms, canceling out common factors, and rearranging the expression to make it easier to understand and work with.

Final Answer

The final answer is βˆ’9x6y2\boxed{\frac{-9x^6}{y^2}}.

Discussion

Simplifying algebraic expressions is an important skill in mathematics, and it involves combining like terms, canceling out common factors, and rearranging the expression to make it easier to understand and work with. In this article, we answered some frequently asked questions related to simplifying algebraic expressions and provided examples of how to simplify expressions by canceling out common factors and rearranging terms.

Related Topics

  • Simplifying algebraic expressions
  • Canceling out common factors
  • Rearranging expressions
  • Multiplying fractions

References

Further Reading