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(a + b)^2 Expansion and Visualisation

Evaluate a+2...

Question

Evaluate
$(a + 2 b) (a - 2 b)$

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Solution

$(a + 2 b) (a - 2 b)$

$= a (a - 2 b) + 2 b (a - 2 b)$

$= a^{2} - 2 a b + 2 a b - 4 b^{2}$

$= a^{2} - 4 b^{2}$

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(a^{2} + 4 b^{2}) (a + 2 b) (a - 2 b)

x = \frac{\sqrt{a + 2 b} + \sqrt{a - 2 b}}{\sqrt{a + 2 b} - \sqrt{a - 2 b}}

, then show that

b x^{2} - a x + b = 0

Q. Geometrically verify the identity:

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

{(\frac{2^{a}}{2^{b}})}^{a + b} \times {(\frac{2^{b}}{2^{c}})}^{b + c} \times {(\frac{2^{c}}{2^{a}})}^{c + a} = 1

Q. Prove that :

{(\frac{2^{a}}{2^{b}})}^{(a + b)} . {(\frac{2^{b}}{2^{c}})}^{(b + c)} . {(\frac{2^{c}}{2^{d}})}^{(c + d)} . {(\frac{2^{d}}{2^{a}})}^{(d + a)} = 1

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