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Simplify the expression: (3 - sqrt(x+9)) * (3 + sqrt(x+9))

April 13, 2026Mathematics

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Answer

-x

4 steps

The image shows the expression:

(3 - \sqrt{x+9}) \times (3 + \sqrt{x+9})

Recognize the form of the expression.
This expression is in the form of a difference of squares, $(a-b)(a+b)$ , where $a=3$ and $b=\sqrt{x+9}$ .
Apply the difference of squares formula.
The formula for the difference of squares is $(a-b)(a+b) = a^2 - b^2$ .
Substitute $a=3$ and $b=\sqrt{x+9}$ into the formula:
$(3)^2 - (\sqrt{x+9})^2$
Simplify the terms.
$9 - (x+9)$
Distribute the negative sign and combine like terms.
$9 - x - 9$ $-x$

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