QuestionMultiply. Assume that all variables represent positive real numbers. $(\sqrt{c}-b)(\sqrt{c}+b)$ $(\sqrt{c}-b)(\sqrt{c}+b)=$ $\square$ (Simplify your answer.)

Studdy Solution

STEP 1

1. We are multiplying two binomials.
2. The expression is in the form of a difference of squares.
3. All variables represent positive real numbers.

STEP 2

1. Recognize the pattern of the difference of squares.
2. Apply the difference of squares formula to simplify the expression.

STEP 3

Recognize that the expression $(\sqrt{c}-b)(\sqrt{c}+b)$ is in the form of a difference of squares, which is given by the formula:
$(a-b)(a+b) = a^2 - b^2$
In this case, $a = \sqrt{c}$ and $b = b$ .

STEP 4

Apply the difference of squares formula:
$(\sqrt{c})^2 - b^2$
Simplify the expression:
$c - b^2$
This is the simplified form of the expression.
The simplified expression is:
$\boxed{c - b^2}$

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