Question

Evaluate the following using appropriate identities

1) (103)³
2) 98x102​

Answer 1

Explanation:

$\bold \color{red}{ \mathfrak{question : }}$

$1) \: \: ( {103)}^{3}$

$2) \: \: \: 98 \times 102$

$\bold \color{blue}{ \mathfrak{solution : }}$

$= ( {103)}^{3}$

use the identity: (a+b)^3 = a^3 + b^3 + 3a^b + 3ab^2.

$= (100 + 3 {)}^{3}$

$= ( {100)}^{3} + ( {3)}^{3} + 3 \times {100}^{2} \times 3 + 3 \times 100 \times {3}^{2}$

$= 1000000 + 27 + 3 \times 10000 \times 3 + 300 \times 9$

$= 1000027 + 90000 + 2700$

$= 1000027 + 92700$

$= 1092727$

$\colorbox{red}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \colorbox{lime}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \colorbox{magenta}{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }$

$= 98 \times 102$

$= (100 - 2)(100 + 2)$

use identity: (a-b)(a+b) = a^2 - b^2.

$= (100 {)}^{2} - (2 {)}^{2}$

$= 10000 - 4$

$= 9996$

Answer 2

Answer:

103 3% and 1 is right answer