Question

Simplify:
$(4 + \sqrt3)(4 - \sqrt3)$
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Answer 1

We have to simplify :-

$(4 + \sqrt3)(4 - \sqrt3)$

We know that -

$(a + b)(a - b) = {a}^{2} - {b}^{2}$

$\implies(4 + \sqrt3)(4 - \sqrt3)$

Now here a = 4 and b = √3

$\implies(4 + \sqrt3)(4 - \sqrt3) = {4}^{2} - {( \sqrt{3}) }^{2}$

$\implies(4 + \sqrt3)(4 - \sqrt3) = 16- 3$

$\implies(4 + \sqrt3)(4 - \sqrt3) = 13$

Answer : 13

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$\large\bf\blue{Additional-Information}$

$\implies{(a+b)^2 = a^2 + b^2 + 2ab}$

$\implies{(a-b)^2 = a^2 + b^2 - 2ab}$

$\implies{(a+b)^3 = a^3 + b^3 + 3ab(a + b)}$

$\implies{(a-b)^3 = a^3 - b^3 - 3ab(a-b)}$

$\implies{(a^3+b^3)= (a+b)(a^2 - ab + b^2)}$

$\implies{(a^3-b^3)= (a-b)(a^2 + ab + b^2)}$

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