Evaluate The Expression When $a=9$.$a^2 - 16$
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Introduction
In mathematics, expressions are a fundamental concept that helps us represent and solve problems. Evaluating an expression means finding its value by substituting the given variables with their respective values. In this article, we will evaluate the expression $a^2 - 16$ when $a=9$.
Understanding the Expression
The given expression is $a^2 - 16$. This expression consists of two terms: $a^2$ and $-16$. The first term is a squared term, which means it is the result of multiplying the variable $a$ by itself. The second term is a constant term, which is a fixed value.
Substituting the Value of a
To evaluate the expression, we need to substitute the value of $a$, which is given as $9$. We will replace $a$ with $9$ in the expression.
Evaluating the Expression
Now that we have substituted the value of $a$, we can evaluate the expression. We will start by evaluating the squared term $a^2$.
Next, we will subtract $16$ from the result.
Conclusion
In this article, we evaluated the expression $a^2 - 16$ when $a=9$. We substituted the value of $a$ in the expression and then evaluated the expression step by step. The final result is $65$.
Frequently Asked Questions
Q: What is the value of $a^2$ when $a=9$?
A: The value of $a^2$ when $a=9$ is $81$.
Q: What is the value of $a^2 - 16$ when $a=9$?
A: The value of $a^2 - 16$ when $a=9$ is $65$.
Q: How do I evaluate an expression in mathematics?
A: To evaluate an expression, you need to substitute the given variables with their respective values and then perform the operations in the correct order.
Step-by-Step Guide to Evaluating Expressions
Step 1: Substitute the Value of the Variable
Replace the variable with its respective value in the expression.
Step 2: Evaluate the Squared Term
If the expression contains a squared term, evaluate it first.
Step 3: Perform the Operations
Perform the operations in the correct order, following the order of operations (PEMDAS).
Step 4: Simplify the Expression
Simplify the expression by combining like terms and performing any remaining operations.
Tips and Tricks
Tip 1: Read the Expression Carefully
Read the expression carefully to understand what operations need to be performed.
Tip 2: Use the Order of Operations
Use the order of operations (PEMDAS) to perform the operations in the correct order.
Tip 3: Simplify the Expression
Simplify the expression by combining like terms and performing any remaining operations.
Conclusion
Evaluating expressions is an essential skill in mathematics that helps us solve problems and represent real-world situations. By following the steps outlined in this article, you can evaluate expressions with confidence and accuracy. Remember to read the expression carefully, use the order of operations, and simplify the expression to get the correct result.
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Introduction
In our previous article, we evaluated the expression $a^2 - 16$ when $a=9$. We also provided a step-by-step guide to evaluating expressions. In this article, we will answer some frequently asked questions about evaluating expressions.
Q&A
Q: What is the order of operations in mathematics?
A: The order of operations in mathematics is PEMDAS, which stands for:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next (e.g., $2^3$).
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate an expression with multiple variables?
A: To evaluate an expression with multiple variables, you need to substitute the values of all the variables in the expression. For example, if you have an expression like $a^2 + b^2$ and you know that $a=3$ and $b=4$, you would substitute these values into the expression to get $3^2 + 4^2$.
Q: What is the difference between an expression and an equation?
A: An expression is a mathematical statement that contains variables and constants, but it does not contain an equal sign. An equation, on the other hand, is a mathematical statement that contains an equal sign and is used to solve for a variable.
Q: How do I simplify an expression?
A: To simplify an expression, you need to combine like terms and perform any remaining operations. For example, if you have an expression like $2x + 3x$, you can combine the like terms to get $5x$.
Q: What is the value of $x^2 + 4x + 4$ when $x=2$?
A: To evaluate this expression, you need to substitute the value of $x$ into the expression. So, $x^2 + 4x + 4$ becomes $2^2 + 4(2) + 4$, which simplifies to $4 + 8 + 4 = 16$.
Q: How do I evaluate an expression with a negative exponent?
A: To evaluate an expression with a negative exponent, you need to use the rule that $a^{-n} = \frac{1}{a^n}$. For example, if you have an expression like $2^{-3}$, you can rewrite it as $\frac{1}{2^3}$, which simplifies to $\frac{1}{8}$.
Q: What is the value of $\frac{1}{x} + 2$ when $x=3$?
A: To evaluate this expression, you need to substitute the value of $x$ into the expression. So, $\frac{1}{x} + 2$ becomes $\frac{1}{3} + 2$, which simplifies to $\frac{7}{3}$.
Conclusion
Evaluating expressions is an essential skill in mathematics that helps us solve problems and represent real-world situations. By following the steps outlined in this article, you can evaluate expressions with confidence and accuracy. Remember to read the expression carefully, use the order of operations, and simplify the expression to get the correct result.
Frequently Asked Questions
Q: What is the value of $a^2 - 16$ when $a=9$?
A: The value of $a^2 - 16$ when $a=9$ is $65$.
Q: How do I evaluate an expression with multiple variables?
A: To evaluate an expression with multiple variables, you need to substitute the values of all the variables in the expression.
Q: What is the difference between an expression and an equation?
A: An expression is a mathematical statement that contains variables and constants, but it does not contain an equal sign. An equation, on the other hand, is a mathematical statement that contains an equal sign and is used to solve for a variable.
Step-by-Step Guide to Evaluating Expressions
Step 1: Substitute the Value of the Variable
Replace the variable with its respective value in the expression.
Step 2: Evaluate the Squared Term
If the expression contains a squared term, evaluate it first.
Step 3: Perform the Operations
Perform the operations in the correct order, following the order of operations (PEMDAS).
Step 4: Simplify the Expression
Simplify the expression by combining like terms and performing any remaining operations.
Tips and Tricks
Tip 1: Read the Expression Carefully
Read the expression carefully to understand what operations need to be performed.
Tip 2: Use the Order of Operations
Use the order of operations (PEMDAS) to perform the operations in the correct order.
Tip 3: Simplify the Expression
Simplify the expression by combining like terms and performing any remaining operations.