When asked to factor the x^2-100, a student gives the answer (x-10) (x-10) What is the wrong with this answer?

A. One of the minus signs should be a plus sign

B. Both minus signs should be plus signs

C. There is nothing wrong with the answers

D. - 1 is also a factor

Hello!

Let's begin by simplifying the expression (x - 10) (x - 10). To expand this, we will use the FOIL method. This method is also known as, first, outer, inner, and last.

This means that, we multiply the first terms, then the outer term, followed by the inner terms, and the last terms.

First: x · x = x²

Outer: - 10 · x = - 10

Inner: - 10 · x = - 10

Last: - 10 · - 10 = 100

Adding up the values equals to: x² - 20x + 100, which is not equivalent is x² - 100.

Since we know that if you multiply a negative by a positive, its quotient is a negative number. If we change one of subtraction signs to a positive sign, it is shown as: - 10 · 10 = - 100, and also, if you add - 10x and 10x together, it will equal zero. This is shown as: (x + 10) (x - 10). Now, let's expand it.

First: x · x = x²

Outer: x · - 10 = - 10

Inner: 10 · x = 10

Last: - 10 · 10 = - 100

Adding the terms together makes the quotient equal to x² - 100.

Therefore, the answer is A, one of the minus signs should be a plus sign.