Question

factor the following binomial.\\(x^2 - 1\\)\\((?x + \square)(\square x - \square)\\)

Explanation:

Step1: Recall difference of squares formula

The difference of squares formula is \(a^2 - b^2=(a + b)(a - b)\).

Step2: Identify \(a\) and \(b\) in \(x^2-1\)

In the binomial \(x^2 - 1\), we have \(a = x\) (since \(a^2=x^2\)) and \(b = 1\) (since \(b^2 = 1\)).

Step3: Apply the formula

Using the difference of squares formula, \(x^2-1=(x + 1)(x - 1)\). Comparing with \(([?]x+\square)(\square x-\square)\), we can see that the coefficients of \(x\) are \(1\), the constant term in the first binomial is \(1\), and the constant term in the second binomial is \(1\).

Answer:

The filled - in form is \((1x + 1)(1x - 1)\)