Remove unnecessary factors

Oct 13, 2025 by talynt.org 68 views

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve complex equations and problems. It involves combining like terms, removing unnecessary factors, and rearranging the expression to make it more manageable. In this article, we will focus on simplifying the given expression, which involves multiplying and combining like terms.

The Given Expression

The given expression is:

${ -8x^6y \times 2x^4y^5 \times \left(-7x^{10}y \cdot 6^2\right) }$

This expression involves multiplying three terms together, each of which contains variables and constants. Our goal is to simplify this expression by combining like terms and removing unnecessary factors.

Step 1: Multiply the Constants

To simplify the expression, we start by multiplying the constants together. The constants in the given expression are -8, 2, and -7. We multiply these numbers together to get:

${ -8 \times 2 \times -7 = 112 }$

So, the constant term in the simplified expression is 112.

Step 2: Multiply the Variables

Next, we multiply the variables together. The variables in the given expression are x^6, x^4, x^10, y, and y^5. We multiply these variables together to get:

${ x^6 \times x^4 \times x^{10} \times y \times y^5 = x^{20}y^6 }$

So, the variable term in the simplified expression is x^20y6.

Step 3: Combine the Terms

Now that we have multiplied the constants and variables together, we can combine the terms to get the simplified expression. We multiply the constant term (112) by the variable term (x^20y6) to get:

${ 112x^{20}y^6 }$

This is the simplified expression.

Simplified Expression

The simplified expression is:

${ 112x^{20}y^6 }$

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

Conclusion

Simplifying expressions is an important skill in algebra, and it involves combining like terms, removing unnecessary factors, and rearranging the expression to make it more manageable. In this article, we simplified the given expression by multiplying the constants and variables together and combining the terms. The simplified expression is 112x^20y6.

Tips and Tricks

Here are some tips and tricks to help you simplify expressions:

Combine like terms: When simplifying an expression, combine like terms by adding or subtracting the coefficients of the variables.
Remove unnecessary factors: Remove any unnecessary factors from the expression by canceling them out.
Rearrange the expression: Rearrange the expression to make it more manageable by grouping like terms together.
Use the distributive property: Use the distributive property to multiply the variables and constants together.

By following these tips and tricks, you can simplify expressions more efficiently and effectively.

Common Mistakes to Avoid

Here are some common mistakes to avoid when simplifying expressions:

Not combining like terms: Failing to combine like terms can lead to a more complex expression.
Not removing unnecessary factors: Failing to remove unnecessary factors can lead to a more complicated expression.
Not rearranging the expression: Failing to rearrange the expression can make it more difficult to work with.
Not using the distributive property: Failing to use the distributive property can lead to a more complicated expression.

By avoiding these common mistakes, you can simplify expressions more effectively and efficiently.

Real-World Applications

Simplifying expressions has many real-world applications, including:

Science and engineering: Simplifying expressions is essential in science and engineering, where complex equations and problems need to be solved.
Finance: Simplifying expressions is also important in finance, where complex financial models and equations need to be solved.
Computer programming: Simplifying expressions is also essential in computer programming, where complex algorithms and equations need to be solved.

By understanding how to simplify expressions, you can apply this skill to a wide range of real-world problems and applications.