Evaluate using identities:a) 1022
b) 501 x 502 c) 1532 – 1472
d) 4.92
Answers
Answer:
Step-by-step explanation:
a) 1022²
= ( 1000 + 22 )² [∵ Identity : ( a + b )² = a² + 2ab +b² ]
= ( 1000 )² + 2 ( 1000 ) ( 22 ) + ( 22 )²
= 1000000 + 44000 + 484
= 1044484 is the answer.
b) 501 × 502
= ( 500 + 1 ) × ( 500 + 2 ) [∵Identity : ( a + b ) × ( a + c ) = a² + (b + c )a + bc ]
= ( 500 )² + ( 1 + 2 ) × 500 + ( 1 × 2 )
= 250000 + ( 3 ) × 500 + 2
= 250000 + 1500 + 2
= 251502 is the answer.
c) 1532 × 1472
= ( 1500 + 32 ) × ( 1500 - 28 ) [∵Identity : (a + b ) × ( a - c ) = a² - (c - b) a - bc ]
= ( 1500 )² - ( 28 - 32 ) × 1500 - ( 32 × 28 )
= 2250000 - ( - 4 ) × 1500 - 896
= 2250000 + 6000 - 896
= 2256000 - 896
= 2255104 is the answer.
d) 4.92²
= ( 4 + 0.92 )² [∵ Identity : (a + b ) ² = a² + 2ab +b² ]
= ( 4 )² + 2 ( 4 ) ( 0.92 ) + ( 0.92 )²
= 16 + 7.36 + 0.8464
= 24.2064 is the answer.