Rút gọn
a)\(6x^5y.\frac{1}{2}x^3yz\)
b)\(6xy+\frac{1}{2}x^2-7xy-3x^2+2y\)
Những câu hỏi liên quan
Rút gọn :a)\(6x^5y.\frac{1}{2}x^3yz\) b)\(6xy+\frac{1}{2}x^2-7xy-3x^2+2y\)
Rút gọn
A=x(5x-3)-x^2(x-1)+x(x^2-62)-10+3x B=x(x^2+x+1)-x^2(x+1)-x+5
C=-3xy(-x+5y)+5y^2(3x-2y)+2(5y^2-3/2x^2y-2)
D=(3-x-6y)(x^2+2xy+4y^2)-3(x^3-8y^3+10)
\(A=5x^2-3x-x^3+x^2+x^3-62x-10+3x\\ A=6x^2-62x-10\\ B=x^3+x^2+x-x^3-x^2-x+5=5\\ C=3x^2y-15xy^2+15xy^2-10y^3+10y^2-3x^2y-4=-4\)
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b: Ta có: \(B=x\left(x^2+x+1\right)-x^2\left(x+1\right)-x+5\)
\(=x^3+x^2+x-x^3-x^2-x+5\)
=5
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\(\frac{5y^2-6x^2+7xy}{3x^2-10y^2+xy}=\frac{A}{x+2y}\)
tìm đa thức A
\(\frac{5y^2-6x^2+7xy}{3x^2-10y^2+xy}=\frac{\left(y+2x\right)\left(5y-3x\right)}{\left(2y+x\right)\left(3x-5y\right)}\)
\(=\frac{-y-2x}{2y+x}\)
Vậy A = - y - 2x
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tìm đa thức biết :
a) A+(3x^2 - 6xy) = 4x^2 + 10xy - 2y^2
b) A - (2xy + 4y^2) = 3x^2 - 6xy + 5y^2
c) (6x^2y^2 - 12xy - 7xy^3) + A = 0
Bài 1:Tính:
a) (2x-y)+(2x-y)+(2x-y)+3y
b) (x+2y)+(x-2y)+(8x-3y)
c) (x+2y)-2(x-2y)-(2x-3y)
Bài 2: Cho 2 đa thức P= 9x²-6xy+3y² và Q= -3x²+7xy-2y²
Tìm đa thức M biết M+2(x²-4y²)+Q=6x²-4xy+5y²+P
Bài 1:
a) (2x - y) + (2x - y) + (2x - y) + 3y
= 3(2x - y) + 3y
= 3(2x - y + 3y)
= 3(2x + 2y)
= 3.2(x + y)
= 6(x + y)
b) (x + 2y) + (x - 2y) + (8x - 3y)
= x + 2y + x - 2y + 8x - 3y
= 9x - 3y
= 3(3x - y)
c) (x + 2y) - 2(x - 2y) - (2x - 3y)
= x + 2y - 2x + 4y - 2x + 3y
= 9y - 3x
= 3(3y - x)
Bài 2:
M + 2(x2 - 4y2) + Q = 6x2 - 4xy + 5y2 + P
M + 2x2 - 8y2 -3x2 + 7xy - 2y2 = 6x2 - 4xy + 5y2 + 9x2 - 6xy + 3y2
M + 2x2 - 3x2 - 6x2 - 9x2 - 8y2 - 2y2 - 5y2 - 3y2 + 7xy + 4xy + 6xy = 0
M - 16x2 - 18y2 + 17xy = 0
M = 16x2 + 18y2 - 17xy
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Rút gọn:
a) 5(3xn-1-yn-1)-3(xn+1+5yn-1)+4(-xn+1+2yn-1)
b) \(\left(\frac{3}{4}x^{n+1}-\frac{1}{2}y^n\right)2xy-\left(\frac{2}{3}x^{n+1}-\frac{5}{6}y^n\right).7xy\)
Phân tích đa thức thành nhân tử:
a) \(7x^3y^2+14x^2y^3+7xy^4\)
b) \(x^2-xy+5x-5y\)
c) \(3x^2-6xy-12+3y^2\)
`a)7x^3y^2+14x^2y^3+7xy^4`
`=7xy^2(x^2+2xy+y^2)`
`=7xy^2(x+y)^2`
______________________________________________
`b)x^2-xy+5x-5y`
`=x(x-y)+5(x-y)`
`=(x-y)(x+5)`
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`c)3x^2-6xy-12+3y^2`
`=3(x^2-2xy-4+y^2)`
`=3[(x-y)^2-4]`
`=3(x-y-2)(x-y+2)`
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a)7x3y2+14x2y3+7xy4
=7xy2(x2+2xy+y2)
=7xy2(x+y)2
b)x2-xy + 5x - 5y
=x(x-y) + 5(x-y)
=(x-y) (x+5)
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Tính
a) \(\frac{x^3+1}{x}.\left(\frac{1}{x+1}+\frac{x-1}{x^2-x+1}\right)\)
b) \(\frac{x^3-3x^2+2x}{3x^2-4x+1}.\left(\frac{x-1}{x}-\frac{2x-6}{x-1}+\frac{x+1}{x-2}\right)\)
c) \(\frac{3x-3y}{2x^2-2xy+2y^2}:\frac{6x^2-12xy+6y^2}{5x^3+5y^3}:\frac{5x}{x-y}\)
a)\(ĐKXĐ:x\ne0;-1\)
Ta có:\(\frac{x^3+1}{x}.\left(\frac{1}{x+1}+\frac{x-1}{x^2-x+1}\right)=\frac{x^3+1}{x}.\frac{\left(x^2-x+1\right)+\left(x+1\right)\left(x-1\right)}{\left(x+1\right)\left(x^2-x+1\right)}\)
\(=\frac{x^3+1}{x}.\frac{x^2-x+1+\left(x^2-1\right)}{x^3+1}=\frac{2x^2-x}{x}=\frac{2x\left(x-1\right)}{x}=2\left(x-1\right)\)
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tính :
\(\frac{1}{1-x}+\frac{1}{1+x}+\frac{2}{1+x^2}+\frac{4}{1+x^2}+\frac{4}{1+x^4}+\frac{8}{1+x^8}+\frac{16}{1+x^{16}}\)
2y-\(\frac{6xy+2y}{3x+2y}+\frac{2y-9x^2}{3x+2y}\)