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Expand the expression using the formula (a−b)² = a² − 2ab + b².

April 18, 2026Mathematics

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Answer

43 - 12\sqrt{7}

3 steps

Expand the expression using the formula $(a-b)^2 = a^2 - 2ab + b^2$ .
Here, $a = \sqrt{7}$ and $b = 6$ .
$(\sqrt{7}-6)^2 = (\sqrt{7})^2 - 2(\sqrt{7})(6) + (6)^2$
Perform the squaring and multiplication operations.
$= 7 - 12\sqrt{7} + 36$
Combine the constant terms.
$= (7 + 36) - 12\sqrt{7}$ $= 43 - 12\sqrt{7}$
The answer in surd form is:
$43 - 12\sqrt{7}$

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