(x^2-4)(x^2+6x+9)

2 min read Jun 17, 2024
(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.