Question

Evaluate the following using the identity a²-b²=(a+b)(a-b)


a)1025²-589² b)666²-555²

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{1025^{2}-589^{2}=7,03,704}}}$

$\green{\tt{\therefore{666^{2}-555^{2}=1,35,531}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies {1025}^{2} - {589}^{2} \\ \\ \tt: \implies {666}^{2} - {555}^{2} \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies {1025}^{2} - {589}^{2} =?\\ \\ \tt: \implies {666}^{2} - {555}^{2} = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies {1025}^{2} - {589}^{2} \\ \\ \tt \circ \: {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ \tt: \implies {1025}^{2} - {589}^{2} = (1025 + 589)(1025 - 589) \\ \\ \tt: \implies {1025}^{2} - {589}^{2} =1614 \times 436 \\ \\ \green{\tt: \implies {1025}^{2} - {589}^{2} =7,03,704} \\ \\ \bold{Similarly : } \\ \tt: \implies {666}^{2} - {555}^{2} \\ \\ \tt: \implies {666}^{2} - {555}^{2} =(666 + 555)(666 - 555) \\ \\ \tt: \implies {666}^{2} - {555}^{2} =1221 \times 111 \\ \\ \green{\tt: \implies {666}^{2} - {555}^{2} =1,35,531}$

Answer 2

${ \bold{ \boxed{ \boxed{ \red{ANSWER}}}}}$

To find :-

(a) 1025² - 589²

(b) 666² - 555²

USED IDENTITY :–

a² - b² = (a+b)(a-b)

${ \bold{ \boxed{ \boxed{ \green{ \bigstar \: solution \: \bigstar}}}}}$

${ \bold{ \orange{(a) \: \: {1025}^{2} - {589}^{2} }}} \\ \\ { \bold{ \blue {now \: \: use \: \: identity - }}} \\ \\ { \bold{ \orange{ = (1025 + 589)(1025 - 589)}}} \\ \\ { \bold{ \orange{ =( 1614)(436)}}} \\ \\ { \bold{ \orange{ = 703704}}} \\ \\ \\ { \bold{ \orange{(b) \: \: \: {666}^{2} - {555}^{2} }}} \\ \\ { \bold{ \blue{now \: \: use \: \: identity - }}} \\ \\ { \bold{ \orange{ = (666 + 555)(666 - 555)}}} \\ \\ { \bold{ \orange{ = (1221)(111)}}} \\ \\ { \bold{ \orange{ = 135531}}}$

${ \bold{ \boxed{ \boxed{ \red{ \mathfrak{ \huge{hope \: \: you \: \: like \: \: it...}}}}}}}$