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a) \(x^2-4x+5+y^2+2y=\left(x^2-4x+4\right)+\left(y^2+2y+1\right)\)
\(=\left(x-2\right)^2+\left(y+1\right)^2\)
b) \(2x^2+y^2-2xy+10x+25=\left(x^2+10x+25\right)+\left(x^2-2xy+y^2\right)\)
\(=\left(x+5\right)^2+\left(x-y\right)^2\)
c) \(2x^2+2y^2=\left(x^2-2xy+y^2\right)+\left(x^2+2xy+y^2\right)=\left(x-y\right)^2+\left(x+y\right)^2\)
1a/ z2 - 6z + 5 - t2 - 4t = z2 - 2 . 3z + 32 - 4 - t2 - 4t = (z2 - 2 . 3z + 32) - (22 + 2 . 2t + t2) = (z - 3)2 - (2 + t)2
b/ x2 - 2xy + 2y2 + 2y2 + 1 = x2 - 2xy + y2 + y2 + 2y + 1 = (x2 - 2xy + y2) + (y2 + 2y + 1) = (x - y)2 + (y + 1)2
c/ 4x2 - 12x - y2 + 2y + 8 = (2x)2 - 12x - y2 + 2y + 32 - 1 = [ (2x)2 - 2 . 3 . 2x + 32 ] - (y2 - 2y + 1) = (2x - 3)2 - (y - 1)2
2a/ (x + y + 4)(x + y - 4) = x2 + xy - 4x + xy + y2 - 4y + 4x + 4y + 16 = x2 + (xy + xy) + (-4x + 4x) + (-4y + 4y) + y2 + 16
= x2 + 2xy + y2 + 42 = (x + y)2 + 42
b/ (x - y + 6)(x + y - 6) = x2 + xy - 6x - xy - y2 + 6y + 6x + 6y - 36 = x2 + (xy - xy) + (-6x + 6x) + (6y + 6y) - y2 - 36
= x2 - y2 + 12y - 62 = x2 - (y2 - 12y + 62) = x2 - (y2 - 2 . 6y + 62) = x2 - (y - 6)2
c/ (y + 2z - 3)(y - 2z - 3) = y2 -2yz - 3y + 2yz - 4z2 - 6z - 3y + 6z + 9 = y2 + (-2yz + 2yz) + (-3y - 3y) + (-6z + 6z) - 4z2 + 9
= y2 - 6y - 4z2 + 9 = (y2 - 6y + 9) - 4z2 = (y - 3)2 - (2z)2
d/ (x + 2y + 3z)(2y + 3z - x) = 2xy + 3xz - x2 + 4y2 + 6yz - 2xy + 6yz + 9z2 - 3xz = (2xy - 2xy) + (3xz - 3xz) - x2 + (6yz + 6yz) + 9z2 + 4y2
= -x2 + 4y2 + 12yz + 9z2 = (4y2 + 12yz + 9z2) - x2 = [ (2y)2 + 2 . 2 . 3yz + (3z)2 ] - x2 = (2y + 3z)2 - x2
67x73 = (70-3)(70+3) = 702 - 32 = 4900 - 9 = 4801.
a) \(16a^2-24ab+9b^2=\left(4a-3b\right)^2.\)
b) \(a^2+4ab+4b^2=\left(a+2b\right)^2\)
TL:
67 x 73 = ( 70 - 3 ) ( 70 + 3 ) = 702 - 32 = 4900 - 9 = 4801
a) \(16a^2\)\(-24ab+9ab=\left(4a-3b\right)^2\)
b) \(a^2\)\(+4ab+4b^2\)\(=\left(a+2b\right)^2\)
~HT~
1)a)x2+10x+26+y2+2y
=(x2+10x+25)+(y2+2y+1)
=(x+5)2+(y+1)2
b)x2-2xy+2y2+2y+1
=(x2-2xy+y2)+(y2+2y+1)
=(x-y)2+(y+1)2
c)z2-6z+13+t2+4t
=(z2-6z+9)+(t2+4t+4)
=(z-3)2+(t+2)2
d)4x2+2z2-4xz-2z+1
=(4x2-4xz+z2)+(z2-2z+1)
=(2x-z)2+(z-1)2
2)a)(x-3)2-4=0
<=>(x-3-2)(x-3+2)=0
<=>(x-5)(x-1)=0
<=>x-5=0 hoặc x-1=0
<=>x=5 hoặc x=1
b)x2-2x=24
<=>x2-2x-24=0
<=>(x2-6x)+(4x-24)=0
<=>x(x-6)+4(x-6)=0
<=>(x-6)(x+4)=0
<=>x-6=0 hoặc x+4=0
<=>x=6 hoặc x=-4
a) x^2 + 10x + 26 + y^2 + 2y
=x2+10x+25+y2+2y+1
=x2+2.x.5+52+y2+2.y.1+12
=(x+5)2+(y+1)2
b)x^2 - 2xy + 2y^2 + 2y +1
=x2-2xy+y2+y2+2y+1
=(x-y)2+(y+1)2
c)z^2 - 6z + 13 + t^2 + 4t
=z2-6z+9+t2+4z+4
=z2-2.z.3+32+t2+2.t.2+22
=(z-3)2+(t+2)2
d)4x^2 + 2z^2 - 4xz - 2z + 1
=4x2-4xz+z2+z2-2z+1
=(2x)2-2.2x.z+z2+z2-2z.1+12
=(2x-z)2+(z-1)2
a) 2x2 + y2 - 2xy + 10x + 25
= (x2 + y2 - 2xy) + (x2 + 10x + 25)
= (x - y)2 + (x + 5)2
các bn xem đúng ko nhé mk làm bừa nên lên olm hỏi lại mọi người giúp giùm câu b) nha!!
5747568568769868986997696976968978907890780
\(x^2+2y^2+2xy-2y+2\)
\(=\left(\frac{x^2}{2}+2xy+2y^2\right)+\left(\frac{x^2}{2}-2x+2\right)\)
\(=\left(\frac{x}{\sqrt{2}}+\sqrt{2}y\right)^2+\left(\frac{x}{\sqrt{2}}-\sqrt{2}\right)^2\)
a) t2 - 8t + x2 - 4x + 20 = ( t2 - 8t + 16 ) + ( x2 - 4x + 4 ) = ( t - 4 )2 + ( x - 2 )2
b) 49t2 + y2 - 10y + 14t + 26 = ( 49t2 + 14t + 1 ) + ( y2 - 10y + 25 ) = ( 7t + 1 )2 + ( y - 5 )2
c) 2x2 + 4y2 - 2x + 4xy + 1 = ( x2 - 2x + 1 ) + ( x2 + 4xy + 4y2 ) = ( x - 1 )2 + ( x + 2y )2 ( thay 2 thành 1 vì 2 khó làm lắm:v )
Câu 1:
a, (x-1).(x2-x+1)
b, (2a+b).(2a-b)
Câu 2:
a,(2x-1).(x2-5x+3)
b,(-x2+4x-1).(-x+4)
c,(-2x-3).(x+4)+(-x+1)
d,(-3).(x+4).(x-7)+2.(x-5).(x+1)
Câu 3:
a,5x2-(2x+1).(x-2)-x.(3x+3)+7
b,(5x-2).(x+1)-(x-3).5x+1-17.(x-2)
Giup mình với
Mình gửi kiểu kia ko được
a) 6xy^3+x^2y^6+9
= (xy^3 + 3)^2
b) x^4-2x^2y+y^2
= (x^2 - y)^2
c) x^6+25-10x^3
= (x^3 - 5)^2
a/ 6xy3+x2y6+9
= (xy3+3)2 bình phương của 1 tổng;cttq: (A+B)2
b/ x4-2x2y+y2
= (x2-y)2 bình phương của 1 hiệu; cttq (A-B)2
c/ x6+25-10x3
=(x3-5)2
a.) \(A=x^2+y^2+1+2xy+2x+2y=\left(x+y+1\right)^2.\)
b.) \(B=u^2+v^2+2u+2v+2\left(u+1\right)\left(v+1\right)+2=u^2+2u+1+2\left(u+1\right)\left(v+1\right)+v^2+2v+1\)
\(B=\left(u+1\right)^2+2\left(u+1\right)\left(v+1\right)+\left(v+1\right)^2=\left(u+1+v+1\right)^2=\left(u+v+2\right)^2\)
Giả sử số tự nhiên a chia cho 7 dư 3. CMR a chia cho 7 dư 2
a) \(M=2x^2+2y^2\)
\(=2x^2+2y^2+2xy-2xy\)
\(=x^2+2xy+y^2+x^2-2xy+y^2\)
\(\Rightarrow M=\left(x+y\right)^2+\left(x-y\right)^2\)
b) \(N=a^2+16a+b^2+6b+73\)
\(=a^2+16a+64+b^2+6b+9\)
\(=\left(a+8\right)^2+\left(b+3\right)^2\)
cảm ơn bn