Question

6. Evaluate :
(i) (103)^2 – (101)^2
(ii) (998)^2 - (2)^2 Please help me with this​

Answer 1

$\leadsto \sf \blue{Solution:-}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\blue \leadsto\sf{ {(103)}^{2} - {(101)}^{2} }$

$\blue \leadsto\sf{ {(100 + 3)}^{2} - {(100 + 1)}^{2} }$

$\blue \leadsto\sf{ {( {100})^{2} +2 \times 100 \times 3 + ({3})^{2}} - { ({100})^{2} + 2 \times 100 \times 1 + ({1})^{2} } }$

$\blue \leadsto\sf{ { {10000} +600 + 9} - { (10000 + 200 + 1) } }$

$\blue \leadsto\sf{ { \cancel{10000} +600 + 9} - {\cancel10000 - 200 - 1 } }$

$\blue \leadsto\sf{ {609} { \: - \: 201 } }$

$\blue \leadsto\sf{ 408 }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\blue \leadsto\sf{ {(998)}^{2} - {(2)}^{2} }$

$\blue \leadsto\sf{ {(1000 - 2)}^{2} - {(2)}^{2} }$

$\blue \leadsto\sf{ {( {1000})^{2} -2 \times 1000 \times 2 + (2)}^{2} - {(2)}^{2} }$

$\blue \leadsto\sf{ {1000000 -4000 + 4 \: - \: } 4 }$

$\blue \leadsto\sf{ {1000000 -4000 + \cancel4 \: - \: } \cancel4 }$

$\blue \leadsto\sf{996000}$