Question

Expand the following and collect like terms: (−x−1)²

a) x² + 2x + 1
b) x² - 2x + 1
c) x² + 2x - 1
d) x² - 2x - 1

Answer 1

To expand and collect like terms for the expression (-x-1)^2, square each term inside the parentheses and then combine like terms to get the expanded expression x^2 + 2x + 1.

Step-by-step explanation:

To expand and collect like terms for the expression (-x-1)^2, we need to square each term inside the parentheses and then combine like terms.

First, let's square -x: (-x)^2 = x^2

Next, let's square -1: (-1)^2 = 1

Now, we can write the expanded expression as x^2 + 2x + 1. Therefore, option a) x^2 + 2x + 1 is the correct expansion and collection of like terms.

To expand the binomial (−x−1)², we can apply the binomial theorem or simply multiply the binomial by itself. In this case, we will use the straightforward multiplication method:

(−x−1)(−x−1) = (−x)² + (−x)(−1) + (−1)(−x) + (−1)²

= x² + x + x + 1

= x² + 2x + 1