Question

Using a²-b²=(a+b)(a-b) find:

i. 51² - 49²

ii. (1.02)² - (0.98)²

Answer 1

i. 51² - 49²
compare with a²-b²
where a = 51 and b = 49
but given a²-b²= (a+b)(a-b) so, place value of a = 51 and b= 49 in equation
51² - 49² = (51 + 49)(51-49)
add 51 + 49 =100 and substract 51- 49 = 2
51² - 49² = 100 x 2 = 200


ii. (1.02)² - (0.98)²
compare with a²-b²
here a= 1.02 and b= 0.98
but given a²-b²= (a+b)(a-b) so, place value of a = 1.02 and b= 0.98 in equation

(1.02)² - (0.98)² = (1.02 + 0.98)(1.02-0.98)
(1.02)² - (0.98)² = 2 x 0.04 = 0.08