Question

Simplify the following expression completely.

(x^2 - x - 6)(x^2 - 2x - 3)

Answer 1

Answer must be in (x - ?)/(x - ?)

Answer 2

Answer must be in binomial factor

Answer 3

To simplify the expression, we can use the distributive property to multiply each term in the first expression by each term in the second expression.

(x^2 - x - 6)(x^2 - 2x - 3)
= x^2(x^2 - 2x - 3) - x(x^2 - 2x - 3) - 6(x^2 - 2x - 3)
= x^4 - 2x^3 - 3x^2 - x^3 + 2x^2 + 3x - 6x^2 + 12x + 18
= x^4 - 3x^3 - 7x^2 + 15x + 18

Therefore, the completely simplified expression is x^4 - 3x^3 - 7x^2 + 15x + 18.

Answer 4

To simplify the expression further, we can factor the expression:

x^4 - 3x^3 - 7x^2 + 15x + 18

Grouping the terms, we have:

(x^4 - 3x^3) - (7x^2 - 15x - 18)

Now, let's factor out common factors from each group:

x^3(x - 3) - 3(7x^2 - 15x - 18)

Next, let's factor the quadratic term inside the parentheses:

7x^2 - 15x - 18 = (7x + 6)(x - 3)

Replacing this back into our expression:

x^3(x - 3) - 3(7x + 6)(x - 3)

We notice that (x - 3) appears in both terms, so we can factor it out:

(x - 3)(x^3 - 3(7x + 6))

Expanding the second factor, we have:

(x - 3)(x^3 - 21x - 18)

Therefore, the completely simplified expression is:

(x - 3)(x^3 - 21x - 18).

Answer 5

My apologies for the misunderstanding. Let's try again.

(x^2 - x - 6)(x^2 - 2x - 3)

To simplify this expression, we can factor each quadratic individually:

(x^2 - x - 6) factors to (x - 3)(x + 2)
(x^2 - 2x - 3) factors to (x - 3)(x + 1)

Now, we can rewrite the expression using these factors:

(x - 3)(x + 2)(x - 3)(x + 1)

We can further simplify this by combining like terms:

(x - 3)(x - 3)(x + 2)(x + 1)

Now, we can write it in the form (x - ?)/(x - ?):

(x - 3)(x - 3)(x + 2)(x + 1) = (x - 3)^2(x + 2)(x + 1)

So, the completely simplified expression is (x - 3)^2(x + 2)(x + 1).