Tính nhanh
a,30x25x7x8
b,75x8x12x14
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a: =16,71*(91+97)-188(6,2+0,67)
=16,71*188-188*(6,2+0,67)
=188(16,71-6,2-0,67)=1849,92
b: 56^2+31^2-13^2+56*62
=(56+31)^2-13^2
=87^2-13^2
=74*100=7400
a: \(2\cdot53\cdot12+4\cdot6\cdot87-3\cdot8\cdot40\)
\(=24\left(53+87-40\right)\)
=2400
b: \(5\cdot7\cdot77+7\cdot60+49\cdot25-45\cdot42\)
\(=35\cdot77+35\cdot12+49\cdot25-45\cdot42\)
\(=35\cdot89+35\left(7\cdot5-9\cdot6\right)\)
\(=35\cdot70=2450\)
a) 2.53.12+4.6.87-3.8.40
=24.53+24.87-24.40
=24.(53+87-40)
=24.100
=2400
b) 5.7.77-7.60+49.25-45.42
=5.7.77-7.60+7.7.25-45.6.7
=7.(5.77-60+7.25-6.45)
=7.230
=1610
`A=1/[1xx2xx3]+1/[2xx3xx4]+1/[3xx4xx5]+....+1/[98xx99xx100]`
`A=1/2xx(2/[1xx2xx3]+2/[2xx3xx4]+2/[3xx4xx5]+....+2/[98xx99xx100])`
`A=1/2xx(1/[1xx2]-1/[2xx3]+1/[2xx3]-1/[3xx4]+1/[3xx4]-1/[4xx5]+....+1/[98xx99]-1/[99xx100])`
`A=1/2xx(1/[1xx2]-1/[99xx100])`
`A=1/2xx(1/2-1/9900)`
`A=1/2xx(4950/9900-1/9900)`
`A=1/2xx4949/9900`
`A=4949/19800`
\(A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{100-98}{98.99.100}\)
\(A=\left(\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{98.99}-\dfrac{1}{99.100}\right):2\)
\(A=\left(\dfrac{1}{2}-\dfrac{1}{6}+\dfrac{1}{12}-\dfrac{1}{20}+...+\dfrac{1}{9702}-\dfrac{1}{990}\right):2\)
\(A=\left(\dfrac{1}{2}-\dfrac{1}{990}\right):2\)
\(A=\dfrac{4949}{9900}:2\)
\(A=\dfrac{4949}{19800}\)
a) \(29.31=\left(30-1\right)\left(30+1\right)=30^2-1=900-1=899\)
b) \(33,3^2-2.33,3.3,3+3,3^2=\left(33,3-3,3\right)^2=30^2=900\)
c) \(20,1.19,9=\left(20+0,1\right)\left(20-0,1\right)=20^2-0,1^2=400-0.01=399,99\)
d) \(37^2+2.37.13+13^2=\left(37+13\right)^2=50^2=2500\)
\(c,=\left(2\sqrt{3}-6\sqrt{2}+5\sqrt{3}\right)\sqrt{3}+5\sqrt{6}\\ =\left(7\sqrt{3}-6\sqrt{2}\right)\sqrt{3}+5\sqrt{6}\\ =21-6\sqrt{6}+5\sqrt{6}=21-\sqrt{6}\\ f,=\sqrt{\dfrac{\left(\sqrt{3}-3\right)^2}{3-\sqrt{3}}}=\sqrt{\dfrac{\left(3-\sqrt{3}\right)^2}{3-\sqrt{3}}}=\sqrt{3-\sqrt{3}}\\ i,=\dfrac{7-4\sqrt{3}+7+4\sqrt{3}}{7^2-\left(4\sqrt{3}\right)^2}=\dfrac{14}{49-48}=\dfrac{14}{1}=14\)
\(e,=2\sqrt{3\cdot2}-2\sqrt{3}\cdot3+2^2-2\cdot2\cdot\sqrt{3}+\left(\sqrt{3}\right)^2+6\sqrt{3}\\ =2\sqrt{6}-6\sqrt{3}+4-4\sqrt{3}+3+6\sqrt{3}\\ =2\sqrt{6}-4\sqrt{3}+7\)
\(=2\sqrt{3.2}-3.2\sqrt{3}+2^2-2.2.\sqrt{3}+\left(\sqrt{3}\right)^2+6\sqrt{3}\)
\(=2\sqrt{6}-6\sqrt{3}+4-4\sqrt{3}+3+6\sqrt{3}\)
\(=2\sqrt{6}-4\sqrt{3}+7\)
`30 xx 25 xx 7 xx8`
`=(30 xx7) xx (25xx8)`
`=210 xx200`
`=42000`
`----`
`75 xx 8 xx 12 xx 14`
`=(75xx8) xx(12xx14)`
`=600xx168`
`=100800`
\(a.30\times25\times7\times8=\left(30\times7\right)\times\left(25\times8\right)=210\times200=42000\)
\(b.75\times8\times12\times14=\left(75\times12\right)\times\left(8\times14\right)=900\times112=100800\)