Question
(a + b + c)² – (a – b – c)² = ?
(a + b + c)² - ((a - b - c)² =?
Answer 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)
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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