Question
(a + b + c)² – (a – b – c)² = ?
(a + b + c)² - ((a - b - c)² =?
A.
B.
C.
D.
Answer A.
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A.(a + b + c)² a²+b²+c²+2ab+2bc+2ca ( a - b - c )² =[ a+ ( - b ) + ( -c ) ]² =a²+(-b)²+(-c)²+2a(-b)+2(-b)(-c)+2(-c)a = a² + b² + c² - 2ab + 2bc - 2ca (a + b + c)²-( a - b - c )² a²+b²+c²+2ab+2bc+2ca - [a² + b² + c² - 2ab + 2bc - 2ca] =a²+b²+c²+2ab+2bc+2ca - a²-b²-c²+2ab-2bc+2ca =4ab+4ac =4a(b+c) So the correct answer is option A.
A.(a + b + c)² a²+b²+c²+2ab+2bc+2ca ( a - b - c )² =[ a+ ( - b ) + ( -c ) ]² =a²+(-b)²+(-c)²+2a(-b)+2(-b)(-c)+2(-c)a = a² + b² + c² - 2ab + 2bc - 2ca (a + b + c)²-( a - b - c )² a²+b²+c²+2ab+2bc+2ca - [a² + b² + c² - 2ab + 2bc - 2ca] =a²+b²+c²+2ab+2bc+2ca - a²-b²-c²+2ab-2bc+2ca =4ab+4ac =4a(b+c) इसलिए सही उत्तर विकल्प A है।
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