(572x7+266)x(366x9-168x18)x(348x6-348)
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348 x 25 + 348 x 74 + 348
=348x(25+74+1)
=348x100
=34800
HT
( 532 x 7 - 266 x 14 ) x ( 532 x 7 + 266 )
= 0 x( 532 x 7 + 266 )
= 0
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.
\(\left(180\div15-132\div11\right)\cdot\left(57869-297\div11\cdot108\right)\)
\(=\left(12-12\right)\cdot\left(57869-297\div11\cdot108\right)\)
\(=0\cdot\left(57869-297\div11\cdot108\right)\)
\(=0\)
Sửa lại bài 2; dòng 11 ( từ đề bài bài 2 ):
\(=\left\{\left[\left(97+1\right)\cdot49\div2\right]+9\right\}\cdot\left(15\cdot4\right)\)
\(=\left(2401+9\right)\cdot\left(15\cdot4\right)\)
\(=2410\cdot\left(15\cdot4\right)\)
\(=2410\cdot60\)
\(=\left(241\cdot10\right)\cdot\left(6\cdot10\right)\)
\(=\left(241\cdot6\right)\cdot\left(10\cdot10\right)\)
\(=1446\cdot10\)
\(=14460\)
a) = 117 x 100 - 17 x 100
= ( 117 - 17 ) x 100
= 100 x 100
= 10000
b) ( 532 x 7 - 266 x 14 ) x ( 532 x 7 + 266 )
= 532 x 7 - 266 x ( 2 x 7 ) x 3990
= 532 x 7 - 266 x 2 x 7 x 3990
= (532 x 7 - 532 x 7) x 3990
= 0 x 3990
= 0
c) 506 x 5 + 1012 + 253 x 6
= 506 x 5 + (506 x 2) + 253 x ( 2 x 3 )
= 506 x 5 + 506 x 2 + 253 x 2 x 3
= 506 x 5 + 506 x 2 + 506 x 3
= 506 x ( 5 + 2 + 3 )
= 506 x 10
= 5060
Có nhiều cách để giải, sau đay là một cách tính:
\(\left(572\cdot7+266\right)\cdot\left(366\cdot9-168\cdot18\right)\cdot\left(348\cdot6-348\right)\)
\(=\left(286\cdot7\cdot2+133\cdot2\right)\cdot\left(366\cdot9-168\cdot2\cdot9\right)\cdot\left(348\cdot6-348\right)\)
\(=\left(2002\cdot2+133\cdot2\right)\cdot\left(366\cdot9-336\cdot9\right)\cdot\left(348\cdot6-348\right)\)
\(=\left[2\cdot\left(2002+133\right)\right]\cdot\left[9\cdot\left(366-336\right)\right]\cdot\left[348\cdot\left(6-1\right)\right]\)
\(=2\cdot2135\cdot9\cdot30\cdot348\cdot5\)
\(=\left(2\cdot5\right)\cdot30\cdot2135\cdot348\cdot9\)
\(=10\cdot30\cdot2135\cdot348\cdot9\)
\(=\left(10\cdot30\cdot9\right)\cdot\left(2135\cdot348\right)\)
\(=\left(300\cdot9\right)\cdot\left(2135\cdot348\right)\)
\(=2700\cdot742980\)
\(=\left(27\cdot100\right)\cdot\left(74298\cdot10\right)\)
\(=\left(27\cdot74298\right)\cdot\left(100\cdot10\right)\)
\(=2006046\cdot1000\)
\(=2006046000\)