Tính nhanh:
a) 732 – 272; b) 372 - 132
c) 20022 – 22
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87 2 + 73 2 – 27 2 - 13 2 = ( 87 2 – 13 2 ) + ( 73 2 – 27 2 )
= (87 + 13)(87 – 13) + (73 + 27)(73 – 27)
= 100.74 + 100.46 = 100(74 + 46) = 100.120 = 12000
Bài 1:
a.
$=(x^3+2^3)-(x^3-2)=2^3+2=10$
b.
$=(x^2+10x+25)-4x(4x^2+12x+9)-(2x-1)(x^2-9)$
$=x^2+10x+25-16x^3-48x^2-36x-(2x^3-18x-x^2+9)$
$=-18x^3-46x^2-8x+16$
2.
a.
$301^2=(300+1)^2=300^2+2.300+1=90000+600+1$
$=90601$
b.
$198^2=(200-2)^2=4(100-1)^2=4(100^2-2.100+1)$
$=4(10000-200+1)=4.9801=39204$
c.
$93.107=(100-7)(100+7)=100^2-7^2$
$=10000-49=9951$
d.
$127^2+146.127+73^2$
$=127^2+2.73.127+73^2$
$=(127+73)^2=200^2=40000$
(589-732)-(589+2011-732)
= 589-732-589-2011+732
= (589-589)+(732-732)-2011
= 0+0-2011
=-2011
\(\left(589-732\right)-\left(589+2011-732\right)\)
\(=589-732-589-2011+732\)
\(=\left(589-589\right)+\left(-732+732\right)-2011\)
\(=-2011\)
a) \(\left(-48\right)+10+\left(-22\right)+\left(-10\right)\)
\(=\left[\left(-48\right)+\left(-22\right)\right]+\left(-10+10\right)\)
\(=-70+0=-70\)
\(a.75^2-50.75+25^2\\ =75^2-2.25.75+25^2\\ =\left(75-25\right)^2=50^2=2500\)
\(b.103.97\\ =\left(100+3\right)\left(100-3\right)\\ =100^2-3^2\\ =9991\)
\(a,75^2-50.75+25^2\\ =75^2-2.75.25+25^2\\ =\left(75+25\right)^2=100^2=10000\\ b,103.97\\ =\left(100+3\right).\left(100-3\right)\\ =100^2-3^2=10000-9=9991\)
a) 732 - 272
= (73 - 27)(73 + 27)
= 46 . 100
= 4600
b) 372 - 132
= (37 - 13)(37 + 13)
= 24 . 50
= 1200
c) 20022 - 22
= (2002 - 2)(2002 + 2)
= 2000 . 2004
= 4008000
a ) 732 - 272 = 432
b ) 372 - 132 = 242
c ) 20022 - 22 = 19982