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Bài 1:
a)\(5x^2y^3-25x^3y^4+10x^3y^3=5x^2y^3\left(1-5xy+2x\right)\)
b)\(x^3-2xy-x^2y+2y^2=\left(x^3-x^2y\right)-\left(2xy-2y^2\right)=x^2\left(x-y\right)-2y\left(x-y\right)=\left(x-y\right)\left(x^2-2y\right)\)
c)Đề sai hoàn toàn
d) \(2x^2+4xy+2y^2-8z^2=2\left(x^2+2xy+y^2-4z^2\right)=2\left[\left(x+y\right)^2-\left(2z\right)^2\right]=2\left(x+y-2z\right)\left(x+y+2z\right)\)e) \(3x-3a+yx-ya=3\left(x-a\right)+y\left(x-a\right)=\left(x-a\right)\left(3+y\right)\)
f)\(\left(x^2+y^2\right)^2-4x^2y^2=\left(x-y\right)^2\left(x+y\right)^2\)
g)\(2x^2-5x+2=2x^2-x-4x+2=x\left(2x-1\right)-2\left(2x-1\right)=\left(2x-1\right)\left(x-2\right)\)
i)\(14x\left(x-y\right)-21y\left(y-x\right)+28z\left(x-y\right)=14x\left(x-y\right)+21y\left(x-y\right)+28z\left(x-y\right)=7\left(x-y\right)\left(2x+3y+4z\right)\)
Bài 1 : Khai triển :
a, \(\left(x+5\right)^2=x^2+10x+25\)
b, \(\left(x-3y\right)^2=x^2-6xy+9y^2\)
c, \(\left(x^2-6z\right)\left(x^2+6z\right)=x^4-36z^2\)
d, \(\left(x+3y\right)^3=x^3+9x^2y+27xy^2+27y^3\)
e, \(27x^3-9y^2+y-\frac{1}{27}=\left(3x-\frac{1}{3}\right)^3\)
g, \(8x^6+12x^4y+6x^2y^2+y^3=\left(2x^2+y\right)\)
h, \(4x^2+12x^4y+6x^22y^2+y^3=\left(\sqrt[3]{4x^2}+y\right)\)
a) (x3 + 8y3) : (2y + x)
= (x + 2y)(x2 - 2xy + 4y2) : (2y + x)
= x2 - 2xy + 4y2
b) (x3 + 3x2y + 3xy2 + y3) : (2x + 2y)
= (x + y)3 : 2(x + y)
= \(\dfrac{\left(x+y\right)^2}{2}\)
c) (6x5y2 - 9x4y3 + 15x3y4) : 3x3y2
= 3x3y2(2x2 - 3xy + 5y2) : 3x3y2
= 2x2 - 3xy + 5y2
1: \(x^4-4+2x^3-4x\)
\(=\left(x^2-2\right)\left(x^2+2\right)+2x\left(x^2-2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
4: \(-6x^3+18x^2+60x\)
\(=-6x\left(x^2-3x-10\right)\)
\(=-6x\left(x-5\right)\left(x+2\right)\)
6: \(x^4+x^3-5x^2-5x\)
\(=x\left(x^3+x^2-5x-5\right)\)
\(=x\left(x+1\right)\left(x^2-5\right)\)
a) \(\dfrac{6x^2y^3-2x^2y+6xy}{6xy}\)
\(=\dfrac{6x^2y^3}{6xy}-\dfrac{2x^2y}{6xy}+\dfrac{6xy}{6xy}\)
\(=xy^2-\dfrac{x}{3}+1\)
b) \(\dfrac{4\left(x+y\right)^3}{2\left(x+y\right)}\)
\(=\dfrac{2\left(x+y\right).2\left(x+y\right)^2}{2\left(x+y\right)}\)
\(=2\left(x+y\right)^2\)
c) \(\dfrac{8x^3+27y^3}{2x+3y}\)
\(=\dfrac{\left(2x\right)^3+\left(3y\right)^3}{2x+3y}\)
\(=\dfrac{\left(2x+3y\right)\left[\left(2x\right)^2-2x.3y+\left(3y\right)^2\right]}{2x+3y}\)
\(=4x^2-6xy+9y^2\)
d) \(\dfrac{48x^4y^3-12x^2y^5+6x^2y^2}{3x^2y^2}\)
\(=\dfrac{48x^4y^3}{3x^2y^2}-\dfrac{12x^2y^5}{3x^2y^2}+\dfrac{6x^2y^2}{3x^2y^2}\)
\(=16x^2y-4y^3+2\)
\(a,=18x^4-24x^3+30x\\ b,=3x^2y+6xy^2+x^2-6xy^2-12y^3-2xy=3x^2y+x^2-12y^3-2xy\\ c,=-3x^2+4xy-2x\\ d,=\left(x-y\right)^2\left[4\left(x-y\right)^3+2\left(x-y\right)-3\right]:\left(x-y\right)^2\\ =4\left(x-y\right)^3+2\left(x-y\right)-3\)
a: \(=18x^4-24x^3+30x^2\)
b: \(=3x^2y+6xy^2+x^2-6xy^2-12y^3-2xy\)
\(=x^2-12y^3+3x^2y-2xy\)