Question

#
$(1.02) {}^{2} - (0.98) {}^{2}$
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Answer 1

(1.02)² - (0.98)²

= (1.02+0.98) (1.02-0.98)

[ using (a) ²-(b) ² = (a-b) (a+b) ]

= 2 x 0.04

= 0.08

Answer 2

Answer: 0.08

Identity to be used:

• a² - b² = ( a + b ) ( a - b )

Here,

• ( 1.02 )² can be written as ( 1.00 + 0.02 )²
• ( 0.98 )² can be written as ( 1.00 - 0.02 )²

Hence we have brought it to the form of the needed identity.

⇒ ( 1.02 )² - ( 0.98 )² = ( 1.00 + 0.02 )² -  ( 1.00 - 0.02 )²

We know that,

⇒ ( a + b )² - ( a - b )² = ( a² + b² + 2ab - a² + 2ab - b² )

⇒ ( a + b )² - ( a - b )² = ( 4ab )

Hence, we get,

⇒ ( 1.00 + 0.02 )² -  ( 1.00 - 0.02 )² = 4 ( 1.00 ) ( 0.02 )

⇒ ( 1.00 + 0.02 )² -  ( 1.00 - 0.02 )² = 0.08