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`x-y=5`
`<=>(x-y)^2=25`
`<=>x^2-2xy+y^2=25`
`<=>15-2xy=25`
`<=>2xy=-10`
`<=>xy=-5`
`=>x^3-y^3`
`=(x-y)(x^2+xy+y^2)`
`=5.(15-5)`
`=5.10=50`
Ta có: \(x-y=5\)
\(\Leftrightarrow x^2+y^2-10xy=25\)
\(\Leftrightarrow15-10xy=25\)
\(\Leftrightarrow10xy=-10\)
hay xy=-1
Ta có: \(x^3-y^3\)
\(=\left(x-y\right)^3+3xy\left(x-y\right)\)
\(=5^3+3\cdot5\cdot\left(-1\right)\)
\(=125-15=110\)
1. C. \(16x^2\left(x-y\right)\)\(-10y\left(y-1\right)\)\(=-2\left(y-x\right)\)\(\left(8x^2+5y\right)\)
2. C. \(\left(x-y\right)\left(x-y-3\right)\)
3. D. \(\left(x-2\right)\left(x+1\right)\)
4. C. \(y\left(x-2\right)\)\(5x\left(x-3\right)\)
5. D. \(3\left(x-2y\right)\)
1. Trong các kết quả sau kết quả nào sai
A. -17x^3y-34x^2y^2+51xy^3=17xy(x^2+2xy-3y^2)
B. x(y-1) +3(y-1)= -(1-y)(x+3)
C. 16x^2(x-y)-10y(y-1)=-2(y-x)(8x^2+5y)
2. Đa thức (x-y)^2+3(y-x) được phân tích thành nhân tử là:
A. (x+y)(x-y+3)
B. (x-y)(2x-2y+3)
C. (x-y)(x-y-3)
D. Cả 3 câu đều sai
3. Kết quả phân tích đa thức x(x-2)+(x-2) thành nhân tử
A. (x-2)x
B. (x-2)^2.x
C. x(2x-4)
D. (x-2)(x+1)
4. Kết quả phân tích 5x^2(xy-2y)-15x(xy-2y) thành nhân tử
A. (xy-2y)(5x^2-15x^2)
B. y(x-2)(5x^2-15x^2)
C. y(x-2)5x(x-3)
D. (xy-2y)5x(x-3)
5. Kết quả phân tích đa thức 3x-6y thành nhân tử là
A. 3(x-6y)
B. 3(3x-y)
C. 3(3x-2y)
D. 3(x-2y)
a) \(5x^2\)\(\left(x-2y\right)\)\(-\)\(15x\)\(\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x^2-15x\right)\)
\(=5x\left(x-2y\right)\left(x-3\right)\)
b) \(3\left(x-y\right)\)\(-\)\(5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
c) \(10x\left(x-y\right)\)\(-\)\(8y\left(y-x\right)\)
\(=\)\(10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(x-y\right)\left(10x+8y\right)\)
\(=2\left(5x+4\right)\left(x-y\right)\)
d) \(x^2\)\(\left(x-5\right)\)\(+\)\(4\)\(\left(5-x\right)\)
\(=x^2\)\(\left(x-5\right)\)\(-\)\(4\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2-4\right)\)
\(=\left(x-5\right)\left(x-2\right)\left(x-2\right)\)
a) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)\)
\(=\left(x-2y\right)\left(5x^2-15x\right)\)
\(=\left(x-2y\right)\left(x-3\right)5x\)
b)\(3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(3+5x\right)\left(x-y\right)\)
c)\(10x\left(x-y\right)-8y\left(y-x\right)\)
\(=10x\left(x-y\right)+8y\left(x-y\right)\)
\(=\left(10x+8y\right)\left(x-y\right)\)
\(=2\left(5x+4y\right)\left(x-y\right)\)
d)\(x^2\left(x-5\right)+4\left(5-x\right)\)
\(=x^2\left(x-5\right)-4\left(x-5\right)\)
\(=\left(x^2-4\right)\left(x-5\right)\)
\(=\left(x-2\right)\left(x+2\right)\left(x-5\right)\)
\(c,=\left(x-y\right)\left(10x^2-15x^3\right)=5x^2\left(2-3x\right)\left(x-y\right)\\ d,=\left(2x-3y\right)\left(5x+15\right)=5\left(x+3\right)\left(2x-3y\right)\)
c: \(10x^2\left(x-y\right)+15x^3\left(y-x\right)\)
\(=10x^2\left(x-y\right)-15x^3\left(x-y\right)\)
\(=5x^2\left(x-y\right)\left(2-3x\right)\)
d: \(5x\left(2x-3y\right)-15\left(3y-2x\right)\)
\(=5x\left(2x-3y\right)+15\left(2x-3y\right)\)
\(=5\left(2x-3y\right)\left(x+3\right)\)
c: \(10x^2\left(x-y\right)+15x^3\left(y-x\right)\)
\(=10x^2\left(x-y\right)-15x^3\left(x-y\right)\)
\(=5x^2\left(2-3x\right)\left(x-y\right)\)
d: \(5x\left(2x-3y\right)-15\left(3y-2x\right)\)
\(=5x\left(2x-3y\right)+15\left(2x-3y\right)\)
\(=5\left(x+3\right)\left(2x-3y\right)\)
\(\left\{{}\begin{matrix}x-y=5\\x^2-y^2=15\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x-y=5\\x+y=3\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=4\\y=-1\end{matrix}\right.\)
\(x^3-y^3=4^3-\left(-1\right)^3=65\)
x2-y2=15
⇒(x-y)(x+y)=15
⇒ 5(x+y)=15
⇒ x+y=3
x-y=5, x+y=3⇒x-y+x+y=5+3
⇒ 2x=8
⇒ x=4
x+y=3 ⇒ 4+y=3
⇒ y=-1
x3-y3=43-(-1)3=64+1=65