Simplify The Expression:$-12x^2y - 3x^2y$

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Introduction

In algebra, simplifying expressions is a crucial skill that helps us to manipulate and solve equations. It involves combining like terms, which are terms that have the same variable raised to the same power. In this article, we will simplify the expression $-12x^2y - 3x^2y$ using basic algebraic rules.

Understanding the Expression

The given expression is $-12x^2y - 3x^2y$. To simplify this expression, we need to identify the like terms. In this case, both terms have the same variable $x^2y$.

Like Terms

Like terms are terms that have the same variable raised to the same power. In the given expression, both terms have the variable $x^2y$. Therefore, we can combine them by adding their coefficients.

Combining Like Terms

To combine like terms, we add their coefficients. The coefficient of the first term is -12, and the coefficient of the second term is -3. When we add these coefficients, we get:

$$-12x^2y - 3x^2y = (-12 - 3)x^2y$$

Simplifying the Expression

Now that we have combined the like terms, we can simplify the expression further. We can rewrite the expression as:

$$(-12 - 3)x^2y = -15x^2y$$

Conclusion

In this article, we simplified the expression $-12x^2y - 3x^2y$ using basic algebraic rules. We identified the like terms, combined them by adding their coefficients, and simplified the expression further. The final simplified expression is $-15x^2y$.

Tips and Tricks

• When simplifying expressions, always look for like terms.
• Combine like terms by adding their coefficients.
• Simplify the expression further by rewriting it in a more compact form.

Examples and Practice

Try simplifying the following expressions:

• $-8x^2y - 2x^2y$
• $-15x^2y + 3x^2y$
• $-20x^2y - 5x^2y$

Answer Key

• $-8x^2y - 2x^2y = (-8 - 2)x^2y = -10x^2y$
• $-15x^2y + 3x^2y = (-15 + 3)x^2y = -12x^2y$
• $-20x^2y - 5x^2y = (-20 - 5)x^2y = -25x^2y$

Conclusion

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Introduction

In our previous article, we simplified the expression $-12x^2y - 3x^2y$ using basic algebraic rules. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. In the expression $-12x^2y - 3x^2y$, both terms have the variable $x^2y$, making them like terms.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable raised to the same power. In the expression $-12x^2y - 3x^2y$, both terms have the variable $x^2y$, making them like terms.

Q: How do I combine like terms?

A: To combine like terms, add their coefficients. In the expression $-12x^2y - 3x^2y$, the coefficients are -12 and -3. When we add these coefficients, we get:

$$-12x^2y - 3x^2y = (-12 - 3)x^2y$$

Q: What is the final simplified expression?

A: The final simplified expression is $-15x^2y$.

Q: Can I simplify expressions with variables raised to different powers?

A: No, you cannot simplify expressions with variables raised to different powers. For example, the expression $-12x^2y - 3x^3y$ cannot be simplified because the variables $x^2y$ and $x^3y$ have different powers.

Q: Can I simplify expressions with different variables?

A: No, you cannot simplify expressions with different variables. For example, the expression $-12x^2y - 3z^2y$ cannot be simplified because the variables $x^2y$ and $z^2y$ are different.

Q: How do I simplify expressions with negative coefficients?

A: To simplify expressions with negative coefficients, follow the same steps as before. For example, the expression $-12x^2y - 3x^2y$ can be simplified as follows:

$$-12x^2y - 3x^2y = (-12 - 3)x^2y = -15x^2y$$

Q: Can I simplify expressions with fractions?

A: Yes, you can simplify expressions with fractions. For example, the expression $-\frac{12}{3}x^2y - x^2y$ can be simplified as follows:

$$-\frac{12}{3}x^2y - x^2y = -4x^2y - x^2y = (-4 - 1)x^2y = -5x^2y$$

Conclusion

Simplifying expressions is an essential skill in algebra. By identifying like terms, combining them, and simplifying the expression further, we can solve equations and manipulate expressions with ease. In this article, we answered some frequently asked questions related to simplifying expressions. We hope that this article has provided you with a better understanding of how to simplify expressions and has given you the confidence to tackle more complex algebraic problems.

Tips and Tricks

• Always look for like terms when simplifying expressions.
• Combine like terms by adding their coefficients.
• Simplify the expression further by rewriting it in a more compact form.
• Be careful when simplifying expressions with negative coefficients and fractions.

Examples and Practice

Try simplifying the following expressions:

• $-8x^2y - 2x^2y$
• $-15x^2y + 3x^2y$
• $-20x^2y - 5x^2y$
• $-\frac{12}{3}x^2y - x^2y$
• $-12x^2y - 3z^2y$

Answer Key

• $-8x^2y - 2x^2y = (-8 - 2)x^2y = -10x^2y$
• $-15x^2y + 3x^2y = (-15 + 3)x^2y = -12x^2y$
• $-20x^2y - 5x^2y = (-20 - 5)x^2y = -25x^2y$
• $-\frac{12}{3}x^2y - x^2y = (-4 - 1)x^2y = -5x^2y$
• $-12x^2y - 3z^2y$ cannot be simplified because the variables $x^2y$ and $z^2y$ are different.