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C= x2 y - \(\dfrac{1}{2}\)xy2 + \(\dfrac{1}{3}\)x2y +\(\dfrac{2}{3}\)xy2 + 1
C=(x2y + \(\dfrac{1}{3}\)x2y )+( - \(\dfrac{1}{2}\)xy2 +\(\dfrac{2}{3}\)xy2)+ 1
C=\(\dfrac{4}{3}\)x2y +\(\dfrac{1}{6}\)xy2+1
=>Bặc: 3
D= xy2z + 3xyz2 - \(\dfrac{1}{5}\)xy2z - \(\dfrac{1}{3}\)xyz2 - 2
D=(xy2z - \(\dfrac{1}{5}\)xy2z )+( 3xyz2 - \(\dfrac{1}{3}\)xyz2) - 2
D=\(\dfrac{4}{5}\)xy2z +\(\dfrac{8}{3}\)xyz2 - 2
=> Bậc :4
E = 3xy5 - x2y + 7xy - 3xy5 + 3x2y - \(\dfrac{1}{2}\)xy + 1
E=(3xy5- 3xy5) + (- x2y + 3x2y) + (7xy - \(\dfrac{1}{2}\)xy)+ 1
E= 2x2y + \(\dfrac{13}{2}\)xy + 1
=> Bậc: 3
K = 5x3 - 4x + 7x2 - 6x3 + 4x + 1
K= (5x3 - 6x3 ) + (- 4x + 4x) +1
K= -1x3 + 1
=>Bậc: 3
F = 12x3y2 - \(\dfrac{3}{7}\)x4y2 + 2xy3 - x3y2 + x4y2 - xy3 - 5
F=( 12x3y2 - x3y2) + (- \(\dfrac{3}{7}\)x4y2 + x4y2) + (2xy3 - xy3) -5
F=11x3y2 + \(\dfrac{4}{7}\)x4y2 + xy3 - 5
=> Bậc :6
CHÚC BN HỌC TỐT ^-^
a) \(a^3+a^2b-a^2c-abc=a^2\left(a+b\right)-ac\left(a+b\right)=a\left(a+b\right)\left(a-c\right)\)
b) mk chỉnh lại đề
\(x^2+2xy+y^2-xz-yz=\left(x+y\right)^2-z\left(x+y\right)=\left(x+y\right)\left(x+y-z\right)\)
c) \(4-x^2-2xy-y^2=4-\left(x+y\right)^2=\left(2-x-y\right)\left(2+x+y\right)\)
d) \(x^2-2xy+y^2-z^2=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
Bài 26:
\(A+B+C=4x^2-5xy+3y^2+3x^2+2xy+y^2-x^2+3xy+2y^2\)
\(=\left(4x^2+3x^2-x^2\right)+\left(-5xy+2xy+3xy\right)+\left(3y^2+y^2+2y^2\right)\)
\(=6x^2+6y^2\)
\(B-C-A=\left(3x^2+2xy+y^2\right)-\left(-x^2+3xy+2y^2\right)-\left(4x^2-5xy+3y^2\right)\)
\(=3x^2+2xy+y^2+x^2-3xy-2y^2-4x^2+5xy-3y^2\)
\(=\left(3x^2-4x^2+x^2\right)+\left(2xy-3xy+5xy\right)+\left(y^2-2y^2-3y^2\right)\)
\(=-4xy-2y^2\)
\(C-A-B=\left(-x^2+3xy+2y^2\right)-\left(4x^2-5xy+3y^2\right)-\left(3x^2+2xy+y^2\right)\)
\(=-x^2+3xy+2y^2-4x^2+5xy-3y^2-3x^2-2xy-y^2\)
\(=\left(-x^2-4x^2-3x^2\right)+\left(3xy+5xy-2xy\right)+\left(2y^2-3y^2-y^2\right)\)
\(=-8x^2+6xy-2y^2\)
cái câu B-C-A ý thì kết quả phải là 4xy-4y^2 chứ
vì: 2xy-3xy+5xy =4 xy
y^2 - 2y^2-3y^2 = -4y^2
=> = 4xy-4y^2
a) \(x^3+3x^2+3x+1=\left(x+1\right)^3\)
b) \(x^3-6x^2+12x-8=\left(x-2\right)^3\)
c) \(x^2-2xy+y^2-16=\left(x-y\right)^2-4^2=\left(x-y+4\right)\left(x-y-4\right)\)
d) \(49-x^2+2xy-y^2=7^2-\left(x-y\right)^2=\left(7+x-y\right)\left(7-x+y\right)\)
I . Trắc Nghiệm
1B . 2D . 3C . 5A
II . Tự luận
2,a,Ta có: A+(x\(^2\)y-2xy\(^2\)+5xy+1)=-2x\(^2\)y+xy\(^2\)-xy-1
\(\Leftrightarrow\) A=(-2x\(^2\)y+xy\(^2\)-xy-1) - (x\(^2\)y-2xy\(^2\)+5xy+1)
=-2x\(^2\)y+xy\(^2\)-xy-1 - x\(^2\)y+2xy\(^2\)-5xy-1
=(-2x\(^2\)y - x\(^2\)y) + (xy\(^2\)+ 2xy\(^2\)) + (-xy - 5xy ) + (-1 - 1)
= -3x\(^2\)y + 3xy\(^2\) - 6xy - 2
b, thay x=1,y=2 vào đa thức A
Ta có A= -3x\(^2\)y + 3xy\(^2\) - 6xy - 2
= -3 . 1\(^2\) . 2 + 3 .1 . 2\(^2\) - 6 . 1 . 2 -2
= -6 + 12 - 12 - 2
= -8
3,Sắp xếp
f(x) =9-x\(^5\)+4x-2x\(^3\)+x\(^2\)-7x\(^4\)
=9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x
g(x) = x\(^5\)-9+2x\(^2\)+7x\(^4\)+2x\(^3\)-3x
=-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x
b,f(x) + g(x)=(9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x) + (-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x)
=9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x
=(9-9)+(-x\(^5\)+x\(^5\))+(-7x\(^4\)+7x\(^4\))+(-2x\(^3\)+2x\(^3\))+(x\(^2\)+2x\(^2\))+(4x-3x)
= 3x\(^2\) + x
g(x)-f(x)=(-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x) - (9-x\(^5\)-7x\(^4\)-2x\(^3\)+x\(^2\)+4x)
=-9+x\(^5\)+7x\(^4\)+2x\(^3\)+2x\(^2\)-3x-9+x\(^5\)+7x\(^4\)+2x \(^3\)-x\(^2\)-4x
=(-9-9)+(x\(^5\)+x\(^5\))+(7x\(^4\)+7x\(^4\))+(2x\(^3\)+2x\(^3\))+(2x\(^2\)-x\(^2\))+(3x-4x)
= -18 + 2x\(^5\) + 14x\(^4\) + 4x\(^3\) + x\(^2\) - x
I . Trắc Nghiệm 1B . 2D . 3C . 5A II . Tự luận 2,a,Ta có: A+(x22y-2xy22+5xy+1)=-2x22y+xy22-xy-1 ⇔⇔ A=(-2x22y+xy22-xy-1) - (x22y-2xy22+5xy+1) =-2x22y+xy22-xy-1 - x22y+2xy22-5xy-1 =(-2x22y - x22y) + (xy22+ 2xy22) + (-xy - 5xy ) + (-1 - 1) = -3x22y + 3xy22 - 6xy - 2 b, thay x=1,y=2 vào đa thức A Ta có A= -3x22y + 3xy22 - 6xy - 2 = -3 . 122 . 2 + 3 .1 . 222 - 6 . 1 . 2 -2 = -6 + 12 - 12 - 2 = -8 3,Sắp xếp f(x) =9-x55+4x-2x33+x22-7x44 =9-x55-7x44-2x33+x22+4x g(x) = x55-9+2x22+7x44+2x33-3x =-9+x55+7x44+2x33+2x22-3x b,f(x) + g(x)=(9-x55-7x44-2x33+x22+4x) + (-9+x55+7x44+2x33+2x22-3x) =9-x55-7x44-2x33+x22+4x-9+x55+7x44+2x33+2x22-3x =(9-9)+(-x55+x55)+(-7x44+7x44)+(-2x33+2x33)+(x22+2x22)+(4x-3x) = 3x22 + x g(x)-f(x)=(-9+x55+7x44+2x33+2x22-3x) - (9-x55-7x44-2x33+x22+4x) =-9+x55+7x44+2x33+2x22-3x-9+x55+7x44+2x 33-x22-4x =(-9-9)+(x55+x55)+(7x44+7x44)+(2x33+2x33)+(2x22-x22)+(3x-4x) = -18 + 2x55 + 14x44 + 4x33 + x22 - x
\(x^2+2xy+x+2y\)
\(=x\left(x+1\right)+2y\left(x+1\right)\)
\(=\left(x+1\right)\left(2y+x\right)\)
\(7x^2-7xy-5x+5y\)
\(=7x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(7x-5\right)\)
a)x2+2xy+x+2y
=(2xy+x2)+(2y+x)
=x(2y+x)+(2y+x)
=(x+1)(2y+x)
b)7x2-7xy-5x+5y
=(5y-7xy)+(7x2-5x)
=y(5-7x)-x(5-7x)
=(5-7x)(y-x)
c)x2-6x+9-9y2
=(x2+3xy-3x)-(3xy+9y2-9y)-(3x+9y-9)
=x(x+3y-3)-3y(x+3y-3)-3(x+3y-3)
=(x-3y-3)(x+3y-3)
d)x3-3x2+3x-1+2(x2-x)
Ta thấy x=1 là nghiệm của đa thức
=>đa thức có 1 hạng tử là x-1
=(x-1)(x2+1)
e) (x+y)(y+z)(z+x)+xyz
đề sai
f)x(y2-z2)+y(z2-x2)
=(xy2+yz2)+(x2y+xz2)
=y(xy+z2)-x(xy+z2)
=(y-x)(xy+z2)