Select The Correct Answer From Each Drop-down Menu.When $p^2-4p$ Is Subtracted From $p^2+p-6$, The Result Is _____. To Get $ P − 9 P-9 P − 9 [/tex], Subtract _____ From This Result.

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Understanding the Problem

When working with algebraic expressions, it's essential to understand the rules of arithmetic operations. In this problem, we are given two expressions: $p^2-4p$ and $p^2+p-6$. We need to subtract the first expression from the second expression to get the result. Then, we need to subtract a certain value from this result to get $p-9$.

Step 1: Subtracting the Expressions

To subtract the expressions, we need to follow the order of operations (PEMDAS):

  1. Parentheses: None
  2. Exponents: None
  3. Multiplication and Division: None
  4. Addition and Subtraction: Subtract the first expression from the second expression

p2+p−6−(p2−4p)p^2+p-6 - (p^2-4p)

Using the distributive property, we can rewrite the expression as:

p2+p−6−p2+4pp^2+p-6 - p^2 + 4p

Now, we can combine like terms:

p−6+4pp-6 + 4p

5p−65p-6

Step 2: Subtracting a Value from the Result

Now, we need to subtract a certain value from the result to get $p-9$. Let's call this value $x$. We can set up an equation:

5p−6−x=p−95p-6 - x = p-9

To solve for $x$, we can add $x$ to both sides of the equation:

5p−6=p−9+x5p-6 = p-9 + x

Now, we can add $6$ to both sides of the equation:

5p=p−3+x5p = p-3 + x

Next, we can subtract $p$ from both sides of the equation:

4p=−3+x4p = -3 + x

Now, we can add $3$ to both sides of the equation:

4p+3=x4p + 3 = x

Conclusion

In this problem, we were given two expressions and asked to subtract one from the other. Then, we were asked to subtract a certain value from the result to get $p-9$. By following the order of operations and using algebraic properties, we were able to solve for the value.

Key Takeaways

  • When subtracting expressions, follow the order of operations (PEMDAS)
  • Use the distributive property to rewrite expressions
  • Combine like terms to simplify expressions
  • Set up equations to solve for unknown values

Practice Problems

  1. Subtract $2x-3$ from $x^2+4x-5$
  2. Subtract $x+2$ from $x^2-3x+1$
  3. Subtract $3x-2$ from $x^2+2x-4$

Answer Key

  1. x2+2x−8x^2+2x-8

  2. x2−4x+3x^2-4x+3

  3. x^2-x-6$<br/>

Q: What is the order of operations in algebra?

A: The order of operations in algebra is PEMDAS, which stands for:

  1. Parentheses: Evaluate expressions inside parentheses first
  2. Exponents: Evaluate any exponential expressions next
  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 algebraic expressions?

A: To simplify algebraic expressions, follow these steps:

  1. Combine like terms: Combine any terms that have the same variable and coefficient
  2. Use the distributive property: Use the distributive property to rewrite expressions
  3. Simplify fractions: Simplify any fractions in the expression
  4. Check for common factors: Check if there are any common factors in the expression that can be canceled out

Q: What is the distributive property in algebra?

A: The distributive property in algebra states that:

a(b+c)=ab+aca(b+c) = ab + ac

This means that you can distribute a single term to multiple terms inside parentheses.

Q: How do I solve equations with variables on both sides?

A: To solve equations with variables on both sides, follow these steps:

  1. Add or subtract the same value to both sides: Add or subtract the same value to both sides of the equation to get the variable on one side
  2. Multiply or divide both sides by the same value: Multiply or divide both sides of the equation by the same value to get the variable on one side
  3. Check your solution: Check your solution by plugging it back into the original equation

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

A: An equation is a statement that says two expressions are equal, such as:

x+3=5x + 3 = 5

An expression, on the other hand, is a group of terms that are combined using mathematical operations, such as:

x+3x + 3

Q: How do I graph algebraic expressions?

A: To graph algebraic expressions, follow these steps:

  1. Identify the type of function: Identify the type of function, such as linear, quadratic, or polynomial
  2. Find the x-intercepts: Find the x-intercepts of the function by setting the function equal to zero and solving for x
  3. Find the y-intercept: Find the y-intercept of the function by plugging in x = 0
  4. Plot the graph: Plot the graph using the x-intercepts and y-intercept

Q: What are some common algebraic expressions?

A: Some common algebraic expressions include:

  • Linear expressions: Expressions that can be written in the form $ax + b$, such as $2x + 3$
  • Quadratic expressions: Expressions that can be written in the form $ax^2 + bx + c$, such as $x^2 + 4x + 4$
  • Polynomial expressions: Expressions that can be written in the form $a_nx^n + a_{n-1}x^{n-1} + \ldots + a_1x + a_0$, such as $x^3 + 2x^2 - 3x + 1$

Conclusion

Algebraic expressions are a fundamental concept in mathematics, and understanding how to simplify, solve, and graph them is essential for success in mathematics and science. By following the steps outlined in this article, you can become proficient in working with algebraic expressions and tackle even the most challenging problems.