Evaluate The Expressions For $x = -1$, $y = 4$, And $z = -2$.1. $x^3 - Yz$2. $y + X^2 Z$

In algebra, evaluating expressions with given variables is a crucial skill that helps in solving mathematical problems. In this article, we will evaluate two algebraic expressions for the given values of $x = -1$, $y = 4$, and $z = -2$.

Expression 1: $x^3 - yz$

To evaluate the expression $x^3 - yz$, we need to substitute the given values of $x$, $y$, and $z$ into the expression.

Step 1: Substitute the values of $x$, $y$, and $z$

We are given that $x = -1$, $y = 4$, and $z = -2$. Substituting these values into the expression, we get:

$(-1)^3 - (4)(-2)$

Step 2: Simplify the expression

Now, let's simplify the expression by evaluating the exponent and the product.

$(-1)^3 = -1$ (since the cube of a negative number is negative)

$(4)(-2) = -8$ (since the product of a positive number and a negative number is negative)

So, the expression becomes:

$-1 - (-8)$

Step 3: Simplify further

Now, let's simplify the expression further by combining the two terms.

$-1 - (-8) = -1 + 8 = 7$

Therefore, the value of the expression $x^3 - yz$ is $7$.

Expression 2: $y + x^2 z$

To evaluate the expression $y + x^2 z$, we need to substitute the given values of $x$, $y$, and $z$ into the expression.

Step 1: Substitute the values of $x$, $y$, and $z$

We are given that $x = -1$, $y = 4$, and $z = -2$. Substituting these values into the expression, we get:

$4 + (-1)^2 (-2)$

Step 2: Simplify the expression

Now, let's simplify the expression by evaluating the exponent and the product.

$(-1)^2 = 1$ (since the square of a negative number is positive)

$(-2) = -2$ (no change)

So, the expression becomes:

$4 + (1)(-2)$

Step 3: Simplify further

Now, let's simplify the expression further by combining the two terms.

$4 + (1)(-2) = 4 - 2 = 2$

Therefore, the value of the expression $y + x^2 z$ is $2$.

Conclusion

In this article, we evaluated two algebraic expressions for the given values of $x = -1$, $y = 4$, and $z = -2$. We used the order of operations to simplify the expressions and found that the value of the first expression is $7$ and the value of the second expression is $2$.

Tips and Tricks

• When evaluating algebraic expressions, always follow the order of operations (PEMDAS).
• Use parentheses to group terms and simplify the expression.
• Simplify the expression by combining like terms.

Practice Problems

Try evaluating the following algebraic expressions for the given values of $x$, $y$, and $z$:

1. $x^2 + yz$
2. $y - xz$
3. $x^3 + y^2 z$

References

• Algebraic Expressions
• Order of Operations
• Simplifying Algebraic Expressions
  Evaluating Algebraic Expressions: Q&A =====================================

In our previous article, we evaluated two algebraic expressions for the given values of $x = -1$, $y = 4$, and $z = -2$. In this article, we will answer some frequently asked questions about evaluating algebraic expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. The acronym PEMDAS is commonly used to remember the order of operations:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., $x^2$).
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify an algebraic expression?

A: To simplify an algebraic expression, follow these steps:

1. Evaluate any exponential expressions.
2. Evaluate any multiplication and division operations from left to right.
3. Evaluate any addition and subtraction operations from left to right.
4. Combine like terms (terms with the same variable and exponent).

Q: What is a like term?

A: A like term is a term with the same variable and exponent. For example, $2x$ and $5x$ are like terms because they both have the variable $x$ with an exponent of 1.

Q: How do I evaluate an expression with multiple variables?

A: To evaluate an expression with multiple variables, substitute the given values of the variables into the expression and simplify.

Q: What is the difference between an expression and an equation?

A: An expression is a mathematical statement that contains variables and constants, but does not contain an equal sign. An equation is a mathematical statement that contains an equal sign and is used to solve for a variable.

Q: How do I solve an equation with multiple variables?

A: To solve an equation with multiple variables, substitute the given values of the variables into the equation and solve for the remaining variable.

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

• $x^2 + y^2$
• $x^3 - yz$
• $y + x^2 z$
• $x^2 - 4y$

Q: How do I evaluate an expression with absolute value?

A: To evaluate an expression with absolute value, follow these steps:

1. Evaluate the expression inside the absolute value bars.
2. If the result is positive, the absolute value is equal to the result.
3. If the result is negative, the absolute value is equal to the negative of the result.

Q: What is the difference between an expression and a formula?

A: An expression is a mathematical statement that contains variables and constants, but does not contain an equal sign. A formula is a mathematical statement that contains an equal sign and is used to describe a relationship between variables.

Conclusion

In this article, we answered some frequently asked questions about evaluating algebraic expressions. We covered topics such as the order of operations, simplifying expressions, and evaluating expressions with multiple variables. We also discussed the difference between an expression and an equation, and how to solve equations with multiple variables.

Tips and Tricks

• Always follow the order of operations when evaluating an expression.
• Use parentheses to group terms and simplify the expression.
• Simplify the expression by combining like terms.
• Use absolute value to evaluate expressions with negative values.

Practice Problems

Try evaluating the following algebraic expressions for the given values of $x$, $y$, and $z$:

1. $x^2 + yz$
2. $y - xz$
3. $x^3 + y^2 z$

References

• Algebraic Expressions
• Order of Operations
• Simplifying Algebraic Expressions