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có lộn đề ko bn ơi
c). 1081.46
d). 1000
e. P=(x−y)(x2+xy+y2)−2y3=x3−y3−2y3=x3−3y3=(12)3−3.(23)3=−5572
Bài 2.
a) 1013 = (100+1)3 = 1003+3.1002.1+3.100.12+13
= 1000000+30000+300+1 = 1030301
b) 2993 = (300-1)3 = 3003-3.3002.1+3.300.12-13
= 27000000 - 270000 + 900 -1 = 26730899
c) 993 = (100-1)3 = 1003-3.1002.1+3.100.12-1
= 1000000 - 30000 + 300 -1 = 970299
\(1,\\ b,A=\left(u-v\right)^3+3uv\left(u+v\right)\\ A=u^3-3u^2v+3uv^2-v^3+3u^2v+3uv^2=u^3-v^3\\ c,6\left(c-d\right)\left(c+d\right)+2\left(c-d\right)^2-\left(c-d\right)^3\\ =6c^2-6d^2+2c^2-4cd+2d^2-c^3+3c^2d-3cd^2+d^3\\ =8c^2-c^3-4d^2-4cd+3c^2d-3cd^2+d^3\)
\(2,\\ a,101^3=\left(100+1\right)^3\\ =100^3+3\cdot10000\cdot1+3\cdot100\cdot1+1\\ =1000000+30000+300+1=1030301\\ b,299^3=\left(300-1\right)^3\\ =300^3-3\cdot90000\cdot1+3\cdot300\cdot1-1\\ =27000000-270000+900-1\\ =26730899\\ c,99^3=\left(100-1\right)^3\\ =100^3-3\cdot10000\cdot1+3\cdot100\cdot1-1\\ =1000000-30000+300-1=970299\)
a. A = (a + b)3 - (a - b)3
A = \(\left[\left(a+b\right)-\left(a-b\right)\right]\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
A = (a + b - a + b)\(\left[a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right]\)
A = 2b(a2 + a2 + a2 + 2ab - 2ab + b2 - b2 + b2)
A = 2b(3a2 + b2)
A = 6a2b + 2b3
Câu 3:
a: \(49^2=2401\)
b: \(51^2=2601\)
c: \(99\cdot100=9900\)
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.
$127^2+146.127+73^2$
$=127^2+2.73.127+73^2$
$=(127+73)^2=200^2=40000$
