(a+2b)²+(a-2b)² .. Solve with identity
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a²+4b²+4ab + a²+4b²-4ab
2a²+8b²
2a²+8b²
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=> (a+2b)²
= a² + (2b)² + 2(a)(2b)
= a² + 4b² + 4ab
=> (a-2b)²
= a² + (2b)² - 2(a)(2b)
= a² + 4b² - 4ab
=> (a+2b)²+(a-2b)²
= a² + 4b² + 4ab + a² + 4b² - 4ab
= 2a² + 8b²
Formulae used :-
(x+y)² = x²+y²+2xy
(x-y)² = x²+y²-2xy
= a² + (2b)² + 2(a)(2b)
= a² + 4b² + 4ab
=> (a-2b)²
= a² + (2b)² - 2(a)(2b)
= a² + 4b² - 4ab
=> (a+2b)²+(a-2b)²
= a² + 4b² + 4ab + a² + 4b² - 4ab
= 2a² + 8b²
Formulae used :-
(x+y)² = x²+y²+2xy
(x-y)² = x²+y²-2xy
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