次の10個の計算問題を工夫して解き、途中の式を記述する。 (1) $103^2$ (2) $48^2$ (3) $26^2 - 24^2$ (4) $47^2 - 43^2$ (5) $7.5^2 - 2.5^2$ (6) $62 \times 58$ (7) $101 \times 99$ (8) $82 \times 63 + 18 \times 63$ (9) $109 \times 109 - 2 \times 106 \times 109 + 106 \times 106$ (10) $3.14 \times 5.5^2 - 3.14 \times 4.5^2$

1. 問題の内容

次の10個の計算問題を工夫して解き、途中の式を記述する。

(1) $103^2$

(2) $48^2$

(3) $26^2 - 24^2$

(4) $47^2 - 43^2$

(5) $7.5^2 - 2.5^2$

(6) $62 \times 58$

(7) $101 \times 99$

(8) $82 \times 63 + 18 \times 63$

(9) $109 \times 109 - 2 \times 106 \times 109 + 106 \times 106$

(10) $3.14 \times 5.5^2 - 3.14 \times 4.5^2$

2. 解き方の手順

(1) $103^2 = (100+3)^2 = 100^2 + 2 \times 100 \times 3 + 3^2 = 10000 + 600 + 9 = 10609$

(2) $48^2 = (50-2)^2 = 50^2 - 2 \times 50 \times 2 + 2^2 = 2500 - 200 + 4 = 2304$

(3) $26^2 - 24^2 = (26+24)(26-24) = 50 \times 2 = 100$

(4) $47^2 - 43^2 = (47+43)(47-43) = 90 \times 4 = 360$

(5) $7.5^2 - 2.5^2 = (7.5+2.5)(7.5-2.5) = 10 \times 5 = 50$

(6) $62 \times 58 = (60+2)(60-2) = 60^2 - 2^2 = 3600 - 4 = 3596$

(7) $101 \times 99 = (100+1)(100-1) = 100^2 - 1^2 = 10000 - 1 = 9999$

(8) $82 \times 63 + 18 \times 63 = (82+18) \times 63 = 100 \times 63 = 6300$

(9) $109 \times 109 - 2 \times 106 \times 109 + 106 \times 106 = 109^2 - 2 \times 106 \times 109 + 106^2 = (109 - 106)^2 = 3^2 = 9$

(10) $3.14 \times 5.5^2 - 3.14 \times 4.5^2 = 3.14 \times (5.5^2 - 4.5^2) = 3.14 \times (5.5+4.5)(5.5-4.5) = 3.14 \times 10 \times 1 = 31.4$

3. 最終的な答え

(1) 10609

(2) 2304

(3) 100

(4) 360

(5) 50

(6) 3596

(7) 9999

(8) 6300

(9) 9

(10) 31.4