An expression is given.

Question

x, squared, minus, 121
2
−121

The expression can be written in the form left parenthesis, x, plus, a, right parenthesis, left parenthesis, x, plus, b, right parenthesis(x+a)(x+b) .

What are the values of a,a and bb ?

Answer 1

The expression given can be rewritten as:

\[ x^2 - 121 \]

This is a difference of squares, which can be factored using the difference of squares formula:

\[ a^2 - b^2 = (a - b)(a + b) \]

In this case, we can identify:

• \( a = x \)
• \( b = 11 \) (since \( 121 = 11^2 \))

Thus, we can factor \( x^2 - 121 \) as:

\[ (x - 11)(x + 11) \]

Hence, in the form \( (x + a)(x + b) \):

• \( a = -11 \)
• \( b = 11 \)

So the values of \( a \) and \( b \) are:

• \( a = -11 \)
• \( b = 11 \)