Simplify This Expression 4p 9 7p 2

Simplify this expression: 4p^9 + 7p^2

This expression appears complicated at first glance, but with the right approach, we can simplify it effortlessly.

Step-by-step simplification:

  • Factor out p^2: We can write 4p^9 as 4p^2 * p^7 and 7p^2 as 7 * p^2. So, our expression becomes: 4p^2(p^7 + 1)

  • Apply the sum of cubes factor formula: The expression inside the parentheses is a sum of cubes, which can be factored as: p^7 + 1 = (p^3)^3 + (1)^3 = (p^3 + 1)(p^6 – p^3 + 1)

Our simplified expression now becomes:

4p^2(p^3 + 1)(p^6 – p^3 + 1)

This form is much easier to work with and can be used for further calculations or analysis.

Simplify This Expression 4p 9 7p 2

Simplifying Algebraic Expressions: A Step-by-Step Guide to 4p³ + 9p + 7p²

Understanding the Concept of Simplifying Expressions

In algebra, simplifying expressions involves combining like terms and eliminating unnecessary symbols or operations to obtain a more concise and manageable form.

Step-by-Step Simplification Process for 4p³ + 9p + 7p²

Step 1: Group Like Terms

The first step is to group terms that contain the same variable raised to the same power. In this case, we have:

  • p³ terms: 4p³
  • p² terms: 7p²
  • p terms: 9p

Step 2: Combine Coefficients

Next, we combine the coefficients of like terms. For instance, the coefficients of the p³ terms are 4, so we simply add them together:

  • p³ terms: 4p³ + 0p³ = 4p³

Similarly, we combine the coefficients of the p² terms:

  • p² terms: 0p² + 7p² = 7p²

And the coefficients of the p terms:

  • p terms: 0p + 9p = 9p

Step 3: Write the Simplified Expression

Finally, we write the simplified expression by combining the like terms:

  • 4p³ + 9p + 7p² = 4p³ + 7p² + 9p

Detailed Demonstration with Embedded Images

Original Expression

Step 1: Group Like Terms

Grouping Like Terms

Step 2: Combine Coefficients

Combined Coefficients

Simplified Expression:

Simplified Expression

Additional Considerations and Examples

Associative Property

  • 4p³ + 9p + 7p² = (4p³ + 7p²) + 9p (Associative property of addition)

Commutative Property

  • 4p³ + 9p + 7p² = 9p + 7p² + 4p³ (Commutative property of addition)

Distributive Property

  • Example 1: 3(2p – 4) = 6p – 12 (Distributive property)
  • Example 2: 2p(p + 3) = 2p² + 6p (Distributive property)

Conclusion

Simplifying algebraic expressions is a crucial skill in algebra that allows us to work with more manageable expressions and solve problems more efficiently. By following the step-by-step process outlined above, we can simplify complex expressions and obtain concise and informative results.

Frequently Asked Questions (FAQs)

  1. Why is simplifying expressions important?
  • Simplifying expressions makes them easier to work with, analyze, and solve problems efficiently.
  1. What are the different methods of simplifying expressions?
  • Grouping like terms, combining coefficients, and applying algebraic properties.
  1. What is the associative property?
  • It states that the grouping of terms in a sum or product does not affect the result.
  1. What is the commutative property?
  • It states that the order of terms in a sum or product can be changed without affecting the result.
  1. Can you provide another example of simplifying an expression?
  • Simplify: 2(3x + 4y) – 5x + 2y
    Solution: 6x + 8y – 5x + 2y = x + 10y

Video How to Simplify an Expression: A Beginner's Guide | Algebraic Expressions | Math with Mr. J