(2n-%E2%80%93-3)(n-%2B-1).jpeg "(2n + 3)(2n – 3)(n + 1)")
Factoring and Simplifying (2n + 3)(2n – 3)(n + 1)
This expression involves the product of three binomials. To simplify it, we'll use the distributive property and some algebraic identities:
1. Recognize the Difference of Squares
Notice that the first two binomials, (2n + 3) and (2n – 3), are in the form of the difference of squares:
- (a + b)(a – b) = a² – b²
Applying this identity:
- (2n + 3)(2n – 3) = (2n)² – (3)² = 4n² – 9
2. Substitute and Expand
Now we have:
- (4n² – 9)(n + 1)
Let's use the distributive property to expand this:
-
4n²(n + 1) – 9(n + 1)
-
4n³ + 4n² – 9n – 9
3. The Final Simplified Form
Therefore, the simplified form of (2n + 3)(2n – 3)(n + 1) is 4n³ + 4n² – 9n – 9.
Key Takeaways:
- Recognizing patterns like the difference of squares can significantly simplify algebraic expressions.
- The distributive property is a fundamental tool for expanding and simplifying expressions.
Note: This expression cannot be factored further. It is a cubic polynomial, and factoring cubic polynomials can be quite complex.