Math Problem Statement

Expand and simplify (x + 3)(x − 3)(2x + 1).

Solution

The question is to expand and simplify the given expression (x+3)(x3)(2x+1)(x + 3)(x - 3)(2x + 1).

Let's break this down step by step:

Step 1: Expand the first two terms (x+3)(x3)(x + 3)(x - 3)

(x+3)(x3)=x29(x + 3)(x - 3) = x^2 - 9 (This is the difference of squares formula: (a+b)(ab)=a2b2(a + b)(a - b) = a^2 - b^2).

Step 2: Multiply the result by (2x+1)(2x + 1)

Now multiply (x29)(x^2 - 9) by (2x+1)(2x + 1): (x29)(2x+1)(x^2 - 9)(2x + 1)

Use the distributive property: =(x2)(2x)+(x2)(1)+(9)(2x)+(9)(1)= (x^2)(2x) + (x^2)(1) + (-9)(2x) + (-9)(1)

Simplify each term: =2x3+x218x9= 2x^3 + x^2 - 18x - 9

Final Answer:

2x3+x218x92x^3 + x^2 - 18x - 9

Would you like a more detailed explanation of any step or help with similar problems? Let me know!


Here are 5 related questions you might find helpful:

  1. How do you apply the distributive property to expand expressions?
  2. What is the difference of squares formula and when do we use it?
  3. How do you simplify expressions involving polynomials?
  4. Can you explain how to handle higher-degree polynomials in expansions?
  5. How do you check your answer when expanding and simplifying?

Tip: Always group like terms carefully to ensure nothing is missed in the final step of simplification!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Polynomials
Simplification
Distributive Property

Formulas

Difference of squares formula: (a + b)(a − b) = a^2 − b^2
Distributive property: a(b + c) = ab + ac

Theorems

-

Suitable Grade Level

Grade 8-10