Question

Tính nhanh 
1.( 572*7+266) * (366*9-168*18)*(346*6-348)
2.(1+3+5+7+...+97+9)*(45*3-15*2-45)
3.(180:15-132:11)*(57869-297:11*108)

Answer 1

1.

\(\left(572\cdot7+266\right)\cdot\left(366\cdot9-168\cdot18\right)\cdot\left(346\cdot6-348\right)\)

\(=\left(286\cdot7\cdot2+133\cdot2\right)\cdot\left(366\cdot9-168\cdot2\cdot9\right)\cdot\left(173\cdot6\cdot2-174\cdot2\right)\)

\(=\left(2002\cdot2+133\cdot2\right)\cdot\left(366\cdot9-336\cdot9\right)\cdot\left(1038\cdot2-174\cdot2\right)\)

\(=\left[2\cdot\left(2002+133\right)\right]\cdot\left[9\cdot\left(366-336\right)\right]\cdot\left[2\cdot\left(1038-174\right)\right]\)

\(=2\cdot2135\cdot9\cdot30\cdot2\cdot864\)

\(=4270\cdot9\cdot30\cdot2\cdot864\)

\(=\left(4270\cdot30\right)\cdot9\cdot2\cdot864\)

\(=\left(427\cdot10\right)\cdot\left(3\cdot10\right)\cdot9\cdot2\cdot864\)

\(=\left(427\cdot3\right)\cdot\left(10\cdot10\right)\cdot9\cdot2\cdot864\)

\(=1281\cdot100\cdot9\cdot2\cdot864\)

\(=\left(1281\cdot100\right)\cdot\left(9\cdot2\cdot864\right)\)

\(=\left(1281\cdot100\right)\cdot15552\)

\(=\left(1281\cdot15552\right)\cdot100\)

\(=19922112\cdot100\)

\(=1992211200\)

2.

\(\left(1+3+5+7+...+97+9\right)\cdot\left(45\cdot3-15\cdot2-45\right)\)

\(=\left(1+3+5+7+...+97+9\right)\cdot\left(15\cdot3\cdot3-15\cdot2-15\cdot3\right)\)

\(=\left(1+3+5+7+...+97+9\right)\cdot\left[15\cdot\left(3\cdot3\right)-15\cdot2-15\cdot3\right]\)

\(=\left(1+3+5+7+...+97+9\right)\cdot\left(15\cdot9-15\cdot2-15\cdot3\right)\)

\(=\left(1+3+5+7+...+97+9\right)\cdot\left[15\cdot\left(9-2-3\right)\right]\)

\(=\left(1+3+5+7+...+97+9\right)\cdot15\cdot4\)

\(=\left[\left(1+3+5+7+...+97\right)+9\right]\cdot\left(15\cdot4\right)\)

Trong \(\left(1+3+5+7+...+97\right)\) có số số hạng là:

        \(\left(97-1\right)\div2+1=49\) ( số hạng )

\(\Rightarrow\left[\left(1+3+5+7+...+97\right)+9\right]\cdot\left(15\cdot4\right)\)

\(=\left[\left(97+1\right)\cdot49\div2\right]\cdot\left(15\cdot4\right)\)

\(=2401\cdot60\)

\(=\left(2401\cdot6\right)\cdot10\)

\(=14406\cdot10\)

\(=144060\)

3.

\(\left(180\div15-132\div11\right)\cdot\left(57869-297\div11\cdot108\right)\)

\(=\left(12-12\right)\cdot\left(57869-297\div11\cdot108\right)\)

\(=0\cdot\left(57869-297\div11\cdot108\right)\)

\(=0\)

Answer 2

Sửa lại bài 2; dòng 11 ( từ đề bài bài 2 ):

\(=\left\{\left[\left(97+1\right)\cdot49\div2\right]+9\right\}\cdot\left(15\cdot4\right)\)

\(=\left(2401+9\right)\cdot\left(15\cdot4\right)\)
\(=2410\cdot\left(15\cdot4\right)\)

\(=2410\cdot60\)

\(=\left(241\cdot10\right)\cdot\left(6\cdot10\right)\)

\(=\left(241\cdot6\right)\cdot\left(10\cdot10\right)\)

\(=1446\cdot10\)

\(=14460\)