Question

What is a square + b square - c square identity??

Answer 1

Answer:

A²+B²+C²=(A+B+C)²-2AB-2BC-2CA.

Answer 2

Therefore the required identity is a² + b² - c² = ( a + b + c )² - 2( c² + ab + bc + ca ).

Given:

The relation to be found out for: a² + b² - c²

To Find:

The expansion identity of a² + b² - c²

Solution:

The given question can be solved very easily as shown below.

Given that: a² + b² - c²

We know that,

⇒ ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

Manipulating the above equation by subtracting 2b² on both sides,

⇒ ( a + b + c )² - 2c² = a² + b² + c² + 2ab + 2bc + 2ca - 2c²

⇒ ( a + b + c )² - 2c² = a² + b² + c² -2c² + 2ab + 2bc + 2ca

⇒ ( a + b + c )² - 2c² = a² + b² - c² + 2ab + 2bc + 2ca

⇒ a² + b² - c² = ( a + b + c )² - 2c² - ( 2ab + 2bc + 2ca )

⇒ a² + b² - c² = ( a + b + c )² - ( 2c² + 2ab + 2bc + 2ca )

⇒ a² + b² - c² = ( a + b + c )² -2( c² + ab + bc + ca )

Therefore the required identity is a² + b² - c² = ( a + b + c )² - 2( c² + ab + bc + ca ).

#SPJ2