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Bài 3:
3: \(6x\left(x-y\right)-9y^2+9xy\)
\(=6x\left(x-y\right)+9xy-9y^2\)
\(=6x\left(x-y\right)+9y\left(x-y\right)\)
\(=\left(x-y\right)\left(6x+9y\right)\)
\(=3\left(2x+3y\right)\left(x-y\right)\)
Bài 4:
a) \(3x^2-3xy-5x+5y\)
\(=\left(3x^2-3xy\right)-\left(5x-5y\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(3x-5\right)\)
b) \(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left[x^2-\left(y+1\right)^2\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
c) \(x^2+1+2x-y^2\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1+y\right)\left(x+1-y\right)\)
d) \(x^2+4x-2xy-4y+y^2\)
\(=\left(x^2-2xy+y^2\right)+\left(4x-4y\right)\)
\(=\left(x-y\right)^2+4\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y+4\right)\)
e) \(x^3-2x^2+x\)
\(=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
f) \(2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x^2+2x+1\right)+y^2\right]\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x-y+1\right)\left(x+y+1\right)\)
a: =3x(x-y)-5(x-y)
=(x-y)(3x-5)
b: \(=2xy\left(x^2-y^2-2y-1\right)\)
\(=2xy\left[x^2-\left(y^2+2y+1\right)\right]\)
\(=2xy\left(x-y-1\right)\left(x+y+1\right)\)
d:
Sửa đề: x^2+4x-2xy-4y+y^2
=x^2-2xy+y^2+4x-4y
=(x-y)^2+4(x-y)
=(x-y)(x-y+4)
e: =x(x^2-2x+1)
=x(x-1)^2
f: =2(x^2+2x+1-y^2)
=2[(x+1)^2-y^2]
=2(x+1+y)(x+1-y)
a: \(=5x^4-4x^3y+10x^3y-8x^2y^2-25x^2y^2+20xy^3-15xy^3+12y^4\)
\(=5x^4+6x^3y-33x^2y^2+5xy^3+12y^4\)
b: \(=\left(x^2-x-2\right)\left(2x-1\right)\)
\(=2x^3-x^2-2x^2+x-4x+2\)
\(=2x^3-3x^2-3x+2\)
c: \(=8x^3+y^3\)
d: \(=a^4-b^4\)
bai2 :cmr
a, a^3+b^3=(a+b)^3-3ab.(a+b)
VP= \(\left(a+b\right)^3-3ab\left(a+b\right)\)
=\(a^3+b^3+3a^2b+3ab^2-3a^2b-3ab^2=a^3+b^3\)
=VT
b.a^3-b^3=(a-b)^3+3ab,(a-b)
\(VP=\left(a-b\right)^3+3ab\left(a-b\right)\)
=\(a^3-3a^2b+ab^2.3-b^3+3a^2b-3ab^2=a^3-b^3\)
=VT
=> ĐPCM
bài 1.
a) = 8x^3+4x^2y+2xy^2-4x^2y-2xy^2-y^3-(8x^3-4x^2y+2xy^2+4x^2y-2xy^2+y^3)
= 8x3+4x2y+2xy2-4x2y-2xy2-y3 - 8x3+4x2y-2xy2-4x2y+2xy2-y3
=-8x2y-6y3
b) = 27x3-18x2y+12xy2+18x2y-12xy2+8y3-27x3
=8y
a. \(x^2\left(5x^3-x-\frac{1}{2}\right)=5x^5-x^3-\frac{x^2}{2}\)
b. \(\left(3xy-x^2+y\right).\frac{2}{3}x^2y=2x^3y^2-\frac{2}{3}x^3y+\frac{2}{3}x^2y^2\)
c.\(\left(4x^3-5xy+2x\right)\left(\frac{-1}{2}xy\right)=-2x^4y+\frac{5}{2}x^2y^2-x^2y\)
a , x(3-x)-y(y-2x)+y(y-2)-x(2y-x)
=3x-x2-y2+2xy+y2-2y-2xy+x2
=3x-(-x2+x2)+(2xy-2xy)-2y
=3x-2y
b,(x2-7)(x+2)-(2x-1)(x-14)+x(x2-2x-22)+35
=x3+2x2-7x-14-2x2+29x-14+x3-2x2-22x+35
=(x3+x3)+(2x2-2x2-2x2)-(-7x+29x-22x)-14-14+35
=2x3-2x2+7
c,(2x+y)(4x2-2xy+y2)-8x3-y3
=2xy2-4x2y+8x3+y3-2xy2+4x2y-8x3-y3
=(2xy2-2xy2)-(-4x2y+4x2y)+(8x3-8x3)+(y3-y3)
=0
lớp 12 bạn