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QuestionSimplify the expression (6+5)(6−5)(\sqrt{6}+5)(\sqrt{6}-5).

Studdy Solution

STEP 1

Assumptions1. We are given two binomial expressions (6+5)(\sqrt{6}+5) and (6−5)(\sqrt{6}-5). . We are asked to find the product of these two binomials.
3. We will use the formula for the product of two binomials, which is (a+b)(a-b) = a^ - b^.

STEP 2

Apply the formula for the product of two binomials to the given expressions.
(6+5)(6−5)=(6)2−(5)2(\sqrt{6}+5)(\sqrt{6}-5) = (\sqrt{6})^2 - (5)^2

STEP 3

Calculate the square of 6\sqrt{6} and 55.
(6)2−(5)2=6−25(\sqrt{6})^2 - (5)^2 =6 -25

STEP 4

Subtract 2525 from 66 to get the final answer.
6−25=−196 -25 = -19So, the product of (6+)(6−)(\sqrt{6}+)(\sqrt{6}-) in simplest form is −19-19.

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