(x%5E2%2B6x%2B9).jpeg "(x^2-4)(x^2+6x+9)")
Factoring and Simplifying (x^2-4)(x^2+6x+9)
This expression involves the multiplication of two quadratic expressions. To simplify it, we can factor each expression and then multiply the resulting factors.
Step 1: Factor the first expression (x^2-4)
This expression is a difference of squares, which can be factored as follows:
- (x^2-4) = (x+2)(x-2)
Step 2: Factor the second expression (x^2+6x+9)
This expression is a perfect square trinomial, which can be factored as follows:
- (x^2+6x+9) = (x+3)(x+3) = (x+3)^2
Step 3: Multiply the factored expressions
Now, we can multiply the factored expressions:
- (x+2)(x-2)(x+3)^2
Final Result:
The simplified expression is (x+2)(x-2)(x+3)^2. This is the factored form of the original expression and cannot be further simplified.
Note: This expression can also be expanded by multiplying the factors together, resulting in a polynomial of degree 4. However, the factored form is generally considered more useful as it allows for easier analysis and manipulation of the expression.