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\(19^2=\left(20-1\right)^2=20^2-2.20.1+1^2=400-40+1=361\)
\(28^2=\left(30-2\right)^2=30^2-2.30.2+2^2=900-120+4=784\)
\(81^2=\left(80+1\right)^2=80^2+2.80.1+1^2=6400+160+1=6561\)
\(91^2=\left(90+1\right)^2=90^2+2.90.1+1^2=8100+180+1=8281\)
\(19.21=\left(20-1\right).\left(20+1\right)=20^2-1^2=400-1=399\)
\(29.31=\left(30-1\right).\left(30+1\right)=30^2-1^2=900-1=899\)
\(39.41=\left(40-1\right).\left(40+1\right)=40^2-1^1=1600-1=1599\)
\(29^2-8^2=\left(29-8\right).\left(29+8\right)=777\)
- 2 phần còn lại bạn cứ làm tương tự :) Vì mk bận nên chỉ giúp đc đến đây thoy <: Chúc bạn học tốt =)
a)
\(19^2=\left(20-1\right)^2=20^2-2.20.1+1^2=400-40+1=361\)
\(28^2=\left(30-2\right)^2=30^2-2.30.2+2^2=900-120+4=784\)
\(81^2=\left(80+1\right)^2=80^2+2.80.1+1^2=6400+160+1=6561\)
\(91^2=\left(90+1\right)^2=90^2+2.90.1+1^2=8100+180+1=8281\)
b)
\(19.21=\left(20-1\right)\left(20+1\right)=20^2-1^2=400-1=399\)
\(29.31=\left(30-1\right)\left(30+1\right)=30^2-1^2=900-1=899\)
\(39.41=\left(40-1\right)\left(40+1\right)=40^2-1^2=1600-1=1599\)
P/s: Lần sau cậu nên chia nhỏ ra đăng nhé!
5:
a: (2x-5)(2x+5)=4x^2-25
b: (3x-5y)(3x+5y)=9x^2-25y^2
c: (3x+7y)(3x-7y)=9x^2-49y^2
d: (2x-1)(2x+1)=4x^2-1
4:
a: 2003*2005=(2004-1)(2004+1)=2004^2-1<2004^2
b: 8(7^2+1)(7^4+1)(7^8+1)
=1/6*(7-1)(7+1)(7^2+1)(7^4+1)(7^8+1)
=1/6(7^2-1)(7^2+1)(7^4+1)(7^8+1)
=1/6(7^16-1)<7^16-1
5:
a: (2x-5)(2x+5)=4x^2-25
b: (3x-5y)(3x+5y)=9x^2-25y^2
c: (3x+7y)(3x-7y)=9x^2-49y^2
d: (2x-1)(2x+1)=4x^2-1
mik chỉ biết bài 5 thôi !
a) 192=(20-1)2=202-2.20.1+12=400-40+1=361;
282=(30-2)2=302-2.30.2+22=900-120+4=784;
812=(80+1)2=802+2.80.1+12=6400+160+1=6561;
912=(90+1)2=902+2.90.1+12=8100+180+1=8281;
b) 19.21=(20-1)(20+1)=202-1=400-1=399;
29.31=(30-1)(30+1)=302-1=900-1=899;
39.41=(40-1)(40+1)=402-1=1600-1=1599
c) 292-82=(29-8)(29+8)=21.37=37(20+1)=740+37=777
562-462=(56-46)(56+46)=10.100=1000
672-562=(67-56)(67+56)=11.123=123(10+1)=1230+123=1353
a) `(3/5 x^2 -1/2 y)^2 = (3/5 x^2)^2 - 2. 3/5 x^2 .1/2 y + (1/2 y)^2`
`= 9/25 x^4 - 3/5 x^2y + 1/4 y^2`
\(\left(\dfrac{1}{3}.x+2y\right)\left(\dfrac{1}{9}x^2-\dfrac{2}{3}xy+4y^2\right)=\left(\dfrac{1}{3}.x\right)^3+\left(2y\right)^3=\dfrac{1}{27}x^3+8y^3\)
b: \(f\left(x\right)=\left(x^2\right)^3-\left(\dfrac{1}{3}\right)^3=x^6-\dfrac{1}{27}\)
a) \(=4x^2-12x+9\)
b) \(=4x^2+2x+\dfrac{1}{4}\)
c) \(=4x^2-\dfrac{4}{3}x+\dfrac{1}{9}\)
\(a,VT=\left(a^2+b^2\right)\left(c^2+d^2\right)=a^2c^2+b^2c^2+a^2d^2+b^2d^2\)
\(VP=\left(ac+bd\right)^2+\left(ad-bc\right)^2=a^2c^2+2abcd+b^2d^2+a^2d^2-2abcd+b^2c^2=a^2c^2+b^2c^2+a^2d^2+b^2d^2\)
\(\Rightarrow VT=a^2c^2+b^2c^2+a^2d^2+b^2d^2=VP\left(đpcm\right)\)
b, Tham khảo:Chứng minh hằng đẳng thức:(a+b+c)3= a3 + b3 + c3 + 3(a+b)(b+c)(c+a) - Hoc24