Question

Simplify : (x - 4)(x ^ 2 - 3x - 9)

a) x ^ 3 - 7x ^ 2 - 21x + 36
b) x ^ 3 - 7x ^ 2 + 3x + 36
c) x ^ 3 - 4x ^ 2 - 12x + 36
d) x ^ 3 + x ^ 2 - 3x - 36​

Answer 1

To simplify the expression (x - 4)(x^2 - 3x - 9), we need to apply the distributive property. This means that we need to multiply each term in the first parentheses by each term in the second parentheses. Let's break it down step-by-step:

First, distribute x from the first parentheses to each term in the second parentheses:

x * x^2 = x^3

x * (-3x) = -3x^2

x * (-9) = -9x

Next, distribute -4 from the first parentheses to each term in the second parentheses:

-4 * x^2 = -4x^2

-4 * (-3x) = 12x

-4 * (-9) = 36

Now, let's combine like terms:

x^3 + (-3x^2) + (-9x) + (-4x^2) + 12x + 36

Combine the x^2 terms: -3x^2 + (-4x^2) = -7x^2

Combine the x terms: -9x + 12x = 3x

The simplified expression is: x^3 - 7x^2 + 3x + 36

Therefore, the correct answer is b) x^3 - 7x^2 + 3x + 36.

Explanation:

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Answer 2

`\sf b) x^3 - 7x^2 + 3x + 36`

Explanation:

Note:

• Binomial: An expression with two terms.
• Distribution: The process of multiplying each term in a binomial by each term in another binomial.
• Combining like terms: Combining terms that have the same variables and exponents.

In this case:

`\sf (x - 4)(x ^ 2 - 3x - 9)`

Distribute the first binomial:

`\sf x(x^2 - 3x - 9) - 4(x^2 - 3x - 9)`

This is because when we multiply a binomial by another binomial, we multiply each term in the first binomial by each term in the second binomial.

Distribute the second binomial:

`\sf x^3 - 3x^2 - 9x - 4x^2 + 12x + 36`

This is because when we distribute a monomial, we multiply each term in the monomial by each term in the binomial.

Combine like terms:

`\sf x^3 - 7x^2 + 3x + 36`

This is because when we combine like terms, we add the coefficients of the terms that have the same variables and exponents.

Therefore, the simplified expression is:

`\sf b) x^3 - 7x^2 + 3x + 36`