Simplify this expression: 4p^9 + 7p^2
This expression appears complicated at first glance, but with the right approach, we can simplify it effortlessly.
Stepbystep 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.
Simplifying Algebraic Expressions: A StepbyStep 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.
StepbyStep 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
Step 1: Group Like Terms
Step 2: Combine Coefficients
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 stepbystep process outlined above, we can simplify complex expressions and obtain concise and informative results.
Frequently Asked Questions (FAQs)
 Why is simplifying expressions important?
 Simplifying expressions makes them easier to work with, analyze, and solve problems efficiently.
 What are the different methods of simplifying expressions?
 Grouping like terms, combining coefficients, and applying algebraic properties.
 What is the associative property?
 It states that the grouping of terms in a sum or product does not affect the result.
 What is the commutative property?
 It states that the order of terms in a sum or product can be changed without affecting the result.
 Can you provide another example of simplifying an expression?
 Simplify: 2(3x + 4y) – 5x + 2y
Solution: 6x + 8y – 5x + 2y = x + 10y
Simplify,This,Expression