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a) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\)
b) sửa đề nhé!
\(6x-9-x^2=-\left(x^2-6x+9\right)\)
\(=-\left(x-3\right)^2\)
a) \([(x-y)3 + (y-z)3]+ (z-x)3\)=\(\left(x-y+y-z\right)\left[\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2\right]-\left(x-z\right)^3\)
\(=\left(x-z\right)\left[\left(\left(x-y\right)^2-\left(x-y\right)\left(y-z\right)+\left(y-z\right)^2-\left(x-z\right)^2\right)\right]\)
\(=\left(x-z\right)\left[\left(x-y\right)\left(x-y-y+z\right)+\left(y-z-x+z\right)\left(y-z+x-z\right)\right]=\left(x-z\right)\left[\left(x-2y+z\right)\left(x+z\right)-\left(x-y\right)\left(x+y-2z\right)\right]\)
\(=\left(x-z\right)\left(x-y\right)\left(x-2y+z-x-y+2z\right)=\left(x-z\right)\left(x-y\right)\left(z-y\right)3\)
b) \(=y^2\left(x^2y-x^3+z^3-z^2y\right)-z^2x^2\left(z-x\right)=y^2\left[-y\left(z^2-x^2\right)-\left(z^3-x^3\right)\right]-z^2x^2\left(z-x\right)\)
\(=y^2\left(z-x\right)\left(-yz-xy-z^2-zx-x^2\right)-z^2x^2\left(z-x\right)=\left(z-x\right)\left(-y^3z-xy^2-z^2y^2-xyz-x^2y^2-z^2x^2\right)\)
đến đây coi như là thành nhân tử rồi nha. em muốn gọn thì ráng ngồi nghĩ rồi tách nha. chỉ cần nhóm mấy cái có ngoặc giống nhau là đc. k khó đâu. chịu khó nghĩ để rèn luyện nha
c) \(x^8+2x^4+1-x^4=\left(x^4+1\right)^2-x^4=\left(x^4+1-x^2\right)\left(x^4+1+x^2\right)\)
\(\left(9a^3-6a^2\right)+\left(6a^2-4a\right)+\left(-9a+6\right)=3a^2\left(3a-2\right)+2a\left(3a-2\right)-3\left(3a-2\right)=\left(3a-2\right)\left(3a^2+2a-3\right)\)
d) em sửa đề đi. đề sai rồi. đồng nhất hệ số phải có dấu bằng nha.
có gì liên hệ chị. đúng nha ;)
\(x^2+6x-y^2+9\)
\(=\left(x^2+6x+9\right)-y^2\)
\(=\left(x+3\right)^2-y^2\)
\(=\left(x+3-y\right)\left(x+3+y\right)\)
1)\(=x^2\left(x-y\right)-y\left(x-y\right)\\ =\left(x-y\right)\left(x^2-y\right)\)
2)\(=\left(x^2+x\right)-\left(2xy+2y\right)\\ =x\left(x+1\right)-2y\left(x+1\right)\\ =\left(x+1\right)\left(x-2y\right)\)
3)\(=\left(x^2+2.x.2y+4y^2\right)-y^2\\ =\left(x+2y\right)^2-y^2\\ =\left(x+2y+y\right)\left(x+2y-y\right)\)
1) x3 - x2y - xy + y2
= (x3 - x2y) - (xy - y2)
= x2.(x - y) - y.(x - y)
= (x - y).(x2 - y)
2) x2 - 2xy + x - 2y
= (x2 + x) - (2xy + 2y)
= x.(x + 1) - 2y.(x + 1)
= (x + 1).(x - 2y)
3) x2 + 4xy + 3y2
= x2 + 3xy + xy + 3y2
= (x2 + 3xy) + (xy + 3y2)
= x.(x + 3y) + y.(x + 3y)
= (x + 3y).(x + y)
1 ) \(x^3-x^2y-xy+y^2\)
\(=\left(x^3-x^2y\right)-\left(xy-y^2\right)\)
\(=x^2.\left(x-y\right)-y.\left(x-y\right)\)
\(=\left(x-y\right).\left(x^2-y\right)\)
2 ) \(x^2-2xy+x-2y\)
\(=\left(x^2+x\right)-\left(2xy+2y\right)\)
\(=x.\left(x+1\right)-2y.\left(x+1\right)\)
\(=\left(x+1\right).\left(x-2y\right)\)
3 ) \(x^2+4xy+3y^2\)
\(=x^2+3xy+xy+3y^2\)
\(=\left(x^2+3xy\right)+\left(xy+3y^2\right)\)
\(=x.\left(x+3y\right)+y.\left(x+3y\right)\)
\(=\left(x+3y\right).\left(x+y\right)\)
x6+3x4y2-8x3y3+3x2y4+y6= x6+3x4y2+3x2y4+y6-8x3y3=(x2+y2)3-(2xy)3
= (x2+y2-2xy)[(x2+y2)2+2xy(x2+y2)+(2xy)2]= (x-y)2(x4+6x2y2+y4+2x3y+2xy3)
(x2+y2-5)2-4x2y2-16xy-16=(x2+y2-5)2-(4x2y2+16xy+16)=(x2+y2-5)2-(2xy+4)2
=(x2+y2-5+2xy+4)(x2+y2-5-2xy-4)=(x2+2xy+y2-1)(x2-2xy+y2-9)=[(x+y)2-1][(x-y)2-32]=(x+y-1)(x+y+1)(x-y-3)(x-y+3)
x4+324=x4+36x2+324-36x2=(x2+18)2-(6x)2=(x2+18-6x)(x2+18+6x)
a) xy – 3x + 2y – 6
= (xy - 3x) + (2y - 6)
= x(y - 3) + 2(y - 3)
= (y - 3)(x + 2)
b) x2y + 4xy + 4y – y3
= y(x2 + 4x + 4 - y2)
= y[(x2 + 4x + 4) - y2]
= y[(x + 2)2 - y2]
= y(x + 2 + y)(x + 2 - y)
c) x2 + y2 + xz + yz + 2xy
= (x2 + 2xy + y2) + (xz + yz)
= (x + y)2 + z(x + y)
= (x + y)(x + y + z)
d) x3 + 3x2 – 3x – 1
= (x3 - 1) + (3x2 - 3x)
= (x - 1)(x2 + x + z) + 3x(x - 1)
= (x - 1)(x2 + 4x + 1)
a )
\(xy-3x+2y-6\)
\(=\left(xy+2y\right)-3x-6\)
\(=y\left(x+2\right)-3\left(x+2\right)\)
\(=\left(y-3\right)\left(x+2\right)\)
b )
\(x^2y+4xy+4y-y^3\)
\(=y\left(x^2+4x+4-y^2\right)\)
\(=y\left[\left(x+2\right)^2-y^2\right]\)
\(=y\left(x+2-y\right)\left(x+2+y\right)\)
c )
\(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
a) \(\left(x-9\right)\left(x-7\right)+1\)
\(=x^2-16x+63+1\)
\(=x^2-16x+64\)
\(=\left(x-8\right)^2\)
b) \(x^3+2x^2-3x-6\)
\(=x^2\left(x+2\right)-3x\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-3x\right)\)
\(=x\left(x+2\right)\left(x-3\right)\)
c) \(x^2-y^2+xz-yz\)
\(=x\left(x+z\right)-y\left(y+z\right)\)
\(=\left(x-y\right)\left(y+z\right)\)
d) \(x^3-x+3x^2y+y^3-y\)
botay:(
mình cũng cần