(6.8)²+2×6.8×3.2+(3.2)²

asked by guest
on Jan 12, 2025 at 5:40 am



You asked:

Evaluate the expression: \({6.8}^{2} + 2 \cdot 6.8 \cdot 3.2 + {3.2}^{2}\)

MathBot Answer:

\[{6.8}^{2} + 2 \cdot 6.8 \cdot 3.2 + {3.2}^{2} = 100\]

\[\begin{aligned}{6.8}^{2} + 2 \cdot 6.8 \cdot 3.2 + {3.2}^{2}& = \left(6 + \frac{8}{10}\right)^{2} + 2 \cdot \left(6 + \frac{8}{10}\right) \cdot \left(3 + \frac{2}{10}\right) + \left(3 + \frac{2}{10}\right)^{2}\\& = \left(6 + \frac{4}{5}\right)^{2} + 2 \cdot \left(6 + \frac{8}{10}\right) \cdot \left(3 + \frac{2}{10}\right) + \left(3 + \frac{2}{10}\right)^{2}\\& = \left(\frac{34}{5}\right)^{2} + 2 \cdot \left(6 + \frac{8}{10}\right) \cdot \left(3 + \frac{2}{10}\right) + \left(3 + \frac{2}{10}\right)^{2}\\& = \frac{1156}{25} + 2 \cdot \left(6 + \frac{8}{10}\right) \cdot \left(3 + \frac{2}{10}\right) + \left(3 + \frac{2}{10}\right)^{2}\\& = \frac{1156}{25} + 2 \cdot \left(6 + \frac{4}{5}\right) \cdot \left(3 + \frac{2}{10}\right) + \left(3 + \frac{2}{10}\right)^{2}\\& = \frac{1156}{25} + 2 \cdot \frac{34}{5} \cdot \left(3 + \frac{2}{10}\right) + \left(3 + \frac{2}{10}\right)^{2}\\& = \frac{1156}{25} + 2 \cdot \frac{34}{5} \cdot \left(3 + \frac{1}{5}\right) + \left(3 + \frac{2}{10}\right)^{2}\\& = \frac{1156}{25} + 2 \cdot \frac{34}{5} \cdot \frac{16}{5} + \left(3 + \frac{2}{10}\right)^{2}\\& = \frac{1156}{25} + \frac{68}{5} \cdot \frac{16}{5} + \left(3 + \frac{2}{10}\right)^{2}\\& = \frac{1156}{25} + \frac{1088}{25} + \left(3 + \frac{2}{10}\right)^{2}\\& = \frac{1156}{25} + \frac{1088}{25} + \left(3 + \frac{1}{5}\right)^{2}\\& = \frac{1156}{25} + \frac{1088}{25} + \left(\frac{16}{5}\right)^{2}\\& = \frac{1156}{25} + \frac{1088}{25} + \frac{256}{25}\\& = \frac{2244}{25} + \frac{256}{25}\\& = 100\end{aligned}\]

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