EDGE Math 8

Example 2

Solve each expression and find the number pattern. Write the next two equations using the obtained pattern.

\begin{array}{l} a . 4^{2} = \\ {(34)}^{2} = \\ {(334)}^{2} = \\ {(3334)}^{2} = \end{array}

\begin{array}{l} b . 9 \times 9 + 7 = \\ 98 \times 9 + 6 = \\ 987 \times 9 + 5 = \\ 9876 \times 9 + 4 = \end{array}

Solution

Look at the patterns.

\begin{array}{l} a . 4^{2} = 16 \\ {(34)}^{2} = 1156 \\ {(334)}^{2} = 111556 \\ {(3334)}^{2} = 11115556 \\ {(33334)}^{2} = 1111155556 \\ {(333334)}^{2} = 111111555556 \end{array}

\begin{array}{l} b . 9 \times 9 + 7 = 88 \\ 98 \times 9 + 6 = 888 \\ 987 \times 9 + 5 = 8888 \\ 9876 \times 9 + 4 = 88 888 \\ 98 765 \times 9 + 3 = 888 888 \\ 987 654 \times 9 + 2 = 8 888 888 \end{array}