Question

- MATHS - 2
Tho simpied value of (****+,c** Y **** ----)
a) x2"
- 12"
b) x?"
d
+
C).x2
2121​

Answer 1

Given expression :

$\sf \bigg( {x}^{ {2}^{n - 1} } + {y}^{ {2}^{n - 1} } \bigg)\bigg( {x}^{ {2}^{n - 1} } - {y}^{ {2}^{n - 1} } \bigg)$

Using algebraic identity ( a + b )( a - b ) = a² - b² we get,

$\Rightarrow \sf \bigg( {x}^{ {2}^{n - 1} } \bigg)^{2} - \bigg({y}^{ {2}^{n - 1} } \bigg)^{2}$

We know that : Law of exponents i. e ( a^m )^n = a^( mn ), So the expression becomes

$\Rightarrow \sf x ^{2^{n - 1} \times 2} - y ^{ {2}^{n - 1} \times 2 }$

Using law of exponent a^m × a^n = a^( m + n) we get,

$\Rightarrow \sf x^{2^{n - 1 + 1} } - y^{ {2}^{n - 1 + 1} }$

$\Rightarrow \sf x^{2^{n } } - y^{ {2}^{n } }$

Hence the value of the given expression is Option (a) x^( 2^n ) - y^( 2^n ).

Additional information :

Algebraic identity : An equation in wich every variable satisfies is said to be an algebraic identity.

E. g

• ( a + b )² = a² + b² + 2ab
• ( a - b )² = a² + b² - 2ab
• ( a + b )( a - b ) = a² - b²
• ( x + a )( x + b) = x² + ( a + b)x + ab
• ( a + b )² - ( a - b )² = 4ab
• ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

Answer 2

Your answer refer to the attachment