Vincen wrote:$$99,999^2-1^2=$$
A. 10^10 - 2
B. (10^5 - 2)^2
C. 10^4(10^5 - 2)
D. 10^5(10^4 - 2)
E. 10^5(10^5 - 2)
One approach:
99,999 = 100,000 - 1 = 10� - 1.
Thus:
99,999² - 1²
=
(10� - 1)² - 1²
=
(10�)² - 2(10�)(1) + 1² - 1²
= (10�)² - 2(10�)
= 10�(10� - 2).
The correct answer is
E.
Alternate approach:
a² - b² = (a+b)(a-b).
Thus:
99,999² - 1²
= (99,999 + 1)(99,999 - 1)
= (100,000)(99,998)
= (10�)(10� - 2).
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