Add: ( − 15 X Z + 4 X Y ) + ( 20 X Y − 9 Y Z + 16 X Z (-15xz + 4xy) + (20xy - 9yz + 16xz ( − 15 X Z + 4 X Y ) + ( 20 X Y − 9 Yz + 16 X Z ]Choose The Correct Simplified Expression:A. 24 X 2 Y 2 − 9 Y Z + X 2 Z 2 24x^2y^2 - 9yz + X^2z^2 24 X 2 Y 2 − 9 Yz + X 2 Z 2 B. 24 X Y − 9 Y Z + X Z 24xy - 9yz + Xz 24 X Y − 9 Yz + X Z C. 16 X Y Z 16xyz 16 X Yz D. 5 X Y − 5 Y Z + 16 X Z 5xy - 5yz + 16xz 5 X Y − 5 Yz + 16 X Z

Understanding the Problem

In algebra, simplifying expressions is a crucial skill that helps us solve equations and inequalities. In this article, we will focus on simplifying a given expression by combining like terms. The expression we will be working with is:

$$(-15xz + 4xy) + (20xy - 9yz + 16xz)$$

Step 1: Identify Like Terms

To simplify the expression, we need to identify like terms. Like terms are terms that have the same variable(s) raised to the same power. In this case, we can identify the following like terms:

• Terms with the variable $x^2y^2$
• Terms with the variable $xy$
• Terms with the variable $yz$
• Terms with the variable $xz$

Step 2: Combine Like Terms

Now that we have identified the like terms, we can combine them. To combine like terms, we add or subtract the coefficients of the terms. The coefficient of a term is the number that is multiplied by the variable(s).

Let's combine the like terms:

• $(-15xz + 16xz)$: This term has the variable $xz$. We can combine the coefficients by adding them: $-15 + 16 = 1$. So, the combined term is $xz$.
• $(4xy + 20xy)$: This term has the variable $xy$. We can combine the coefficients by adding them: $4 + 20 = 24$. So, the combined term is $24xy$.
• $(-9yz)$: This term has the variable $yz$. It is already simplified, so we don't need to do anything.
• $(0)$: This term has the variable $x^2y^2$. It is already simplified, so we don't need to do anything.

Step 3: Write the Simplified Expression

Now that we have combined the like terms, we can write the simplified expression:

$$24xy - 9yz + xz$$

Conclusion

In this article, we learned how to simplify an algebraic expression by combining like terms. We identified the like terms, combined them, and wrote the simplified expression. The correct simplified expression is:

$$24xy - 9yz + xz$$

This expression is the result of combining the like terms in the original expression.

Answer

The correct answer is:

B. $24xy - 9yz + xz$

Additional Examples

Here are some additional examples of simplifying algebraic expressions:

• Simplify the expression: $(3x^2y + 2x^2y) + (5x^2y - 2x^2y)$
• Simplify the expression: $(4xy - 3xy) + (2xy + 5xy)$
• Simplify the expression: $(6x^2y^2 + 2x^2y^2) + (3x^2y^2 - 4x^2y^2)$

Tips and Tricks

Here are some tips and tricks for simplifying algebraic expressions:

• Make sure to identify all the like terms in the expression.
• Combine the like terms by adding or subtracting the coefficients.
• Simplify each term separately before combining them.
• Use the distributive property to simplify expressions with parentheses.

Common Mistakes

Here are some common mistakes to avoid when simplifying algebraic expressions:

• Failing to identify all the like terms in the expression.
• Not combining the like terms correctly.
• Simplifying each term separately without combining them.
• Not using the distributive property to simplify expressions with parentheses.

Conclusion

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

A: The first step in simplifying an algebraic expression is to identify the like terms. Like terms are terms that have the same variable(s) raised to the same power.

Q: How do I identify like terms?

A: To identify like terms, look for terms that have the same variable(s) raised to the same power. For example, in the expression $3x^2y + 2x^2y$, the terms $3x^2y$ and $2x^2y$ are like terms because they both have the variable $x^2y$.

Q: What is the next step after identifying like terms?

A: After identifying like terms, the next step is to combine them. To combine like terms, add or subtract the coefficients of the terms.

Q: How do I combine like terms?

A: To combine like terms, add or subtract the coefficients of the terms. For example, in the expression $3x^2y + 2x^2y$, the coefficients are 3 and 2. To combine them, add 3 and 2, which gives 5. So, the combined term is $5x^2y$.

Q: What if I have a term with a negative coefficient?

A: If you have a term with a negative coefficient, you can combine it with other like terms by adding or subtracting the coefficients. For example, in the expression $-3x^2y + 2x^2y$, the coefficients are -3 and 2. To combine them, add -3 and 2, which gives -1. So, the combined term is $-x^2y$.

Q: Can I simplify an expression with parentheses?

A: Yes, you can simplify an expression with parentheses by using the distributive property. The distributive property states that for any numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$.

Q: How do I use the distributive property to simplify an expression with parentheses?

A: To use the distributive property to simplify an expression with parentheses, multiply the term outside the parentheses by each term inside the parentheses. For example, in the expression $(3x^2y + 2x^2y) + (5x^2y - 2x^2y)$, you can use the distributive property to simplify the expression by multiplying the term outside the parentheses by each term inside the parentheses.

Q: What if I have a term with a variable raised to a power?

A: If you have a term with a variable raised to a power, you can simplify it by combining it with other like terms. For example, in the expression $x^2y + x^2y$, the terms $x^2y$ and $x^2y$ are like terms because they both have the variable $x^2y$. To combine them, add the coefficients, which gives 2. So, the combined term is $2x^2y$.

Q: Can I simplify an expression with fractions?

A: Yes, you can simplify an expression with fractions by combining the fractions. To combine fractions, find a common denominator and add or subtract the numerators.

Q: How do I combine fractions?

A: To combine fractions, find a common denominator and add or subtract the numerators. For example, in the expression $\frac{1}{2} + \frac{1}{3}$, the common denominator is 6. To combine the fractions, add the numerators, which gives $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.

Q: What if I have a term with a negative exponent?

A: If you have a term with a negative exponent, you can simplify it by rewriting the term with a positive exponent. For example, in the expression $x^{-2}$, you can rewrite the term as $\frac{1}{x^2}$.

Conclusion

In conclusion, simplifying algebraic expressions is an important skill that helps us solve equations and inequalities. By identifying like terms, combining them, and using the distributive property, we can simplify complex expressions and make them easier to work with. Remember to make sure to identify all the like terms, combine them correctly, and simplify each term separately before combining them.