$1.02^{2}-0.98^{2}$

asked by guest
on Jan 23, 2025 at 7:27 am



You asked:

Evaluate the expression: \({1.02}^{2} - {0.98}^{2}\)

MathBot Answer:

\[{1.02}^{2} - {0.98}^{2} = \frac{2}{25} = 0.08\]

\[\begin{aligned}{1.02}^{2} - {0.98}^{2}& = \left(1 + \frac{2}{100}\right)^{2} - \left(\frac{98}{100}\right)^{2}\\& = \left(1 + \frac{1}{50}\right)^{2} - \left(\frac{98}{100}\right)^{2}\\& = \left(\frac{51}{50}\right)^{2} - \left(\frac{98}{100}\right)^{2}\\& = \frac{2601}{2500} - \left(\frac{98}{100}\right)^{2}\\& = \frac{2601}{2500} - \left(\frac{49}{50}\right)^{2}\\& = \frac{2601}{2500} - \frac{2401}{2500}\\& = \frac{2}{25}\end{aligned}\]

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