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\(a,14x^2y-21xy^2+28x^2y^2=7xy\left(x-3y+4xy\right)\\ b,x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\\ c,10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=\left(x-y\right)\left(10x+8\right)=2\left(x-y\right)\left(5x+4\right)\)
\(d,\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)\(e,x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)+3xyz-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)
vào bệnh viện hoặc đến nơi khám chữa bệnh gần nhà nhất ko kịp thì die
a) 3( x - y ) - 5x( y - x )
= 3( x - y ) - 5x[ -( x - y ) ]
= 3( x - y ) + 5x( x - y )
= ( 3 + 5x )( x - y )
b) x3 + 2x2y + xy2 - 9x
= x( x2 + 2xy + y2 - 9 )
= x[ ( x + y )2 - 32 ]
= x( x + y - 3 )( x + y + 3 )
c) 14x2y - 21xy2 + 28x2y2
= 7xy( 2x - 3y + 4xy )
Bài giải
\(a,\text{ }3\left(x-y\right)-5x\left(y-x\right)\)
\(=3\left(x-y\right)+5x\left(x-y\right)\)
\(=\left(x-y\right)\left(3+5x\right)\)
\(b,\text{ }x^3+2x^2y+xy^2-9x\)
\(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-3^2\right]\)
\(=x\left(x+y+3\right)\left(x+y-3\right)\)
\(c,\text{ }14x^2y-21xy^2+28x^2y\)
\(=7xy\left(2x-3y+4x\right)\)
\(=7xy\left(6x-3y\right)\)
a) (x - 3)3 + 3 - x
= (x - 3)3 - (x - 3)
= (x - 3)[(x - 3)2 - 1]
= (x - 3)(x - 3 - 1)(x - 3 + 1)
= (x - 3)(x - 4)(x - 2).
b) 33(2y - 3z) - 15x(2y - 3z)2
= 27(2y - 3z) - 15x(2y - 3z)2
= 3(2y - 3z)[9 - 5x(2y - 3z)]
= 3(2y - 3z)(9 - 10xy + 15xz)
d) 18x2(3 + x) + 3(x + 3)
= (x + 3)(18x2 + 3)
= 3(x + 3)(6x2 + 1).
a, (x-3)\(^3\) + 3-x
= (x-3)\(^3\) - (x-3)
= (x-3)*[(x-3)\(^2\) -1]
= (x-3)* ( x\(^2\) - 6x + 9 -1)
= (x-3)*(x\(^2\) - 6x +8)
= (x-3)*[(x\(^2\) -2x) - (4x - 8)]
= (x-3)*[x(x-2) - 4(x-2)]
= (x-3)*(x-2)*(x-4)
b, 3\(^3\)(2y-3z) - 15x(2y-3z)\(^2\)
= (2y-3z) *[3\(^3\) -15x(2y-3z)]
= (2y - 3z)*(27 -30xy +45xz)
= (2y -3z)*3*(9 -10xy +15xz)
= 3*(2y-3z)*(9-10xy+15xz)
c, đề sai
d, 18x\(^2\)(3+x) + 3(x+3)
= 18x\(^2\)(x+3) +3(x+3)
= (x+3)(18x\(^2\) +3)
= (x+3)*3*[(3x)\(^2\) +1)]
= 3(x+3)*[(3x)\(^2\) +1)]
a) = (x + 3)2 - y2 = (x + 3 - y)(x + 3 + y)
b) = x2(x - 3) -4(x - 3) = (x - 3)(x2 - 4) = (x - 3)(x - 2)(x + 2)
c) = 3x(x - y) - 5(x - y) = (x - y)(3x - y)
d) Nhầm đề. tui sửa lại x3 + y3 + 2x2 - 2xy + 2y2
= x3 + y3 + 2(x2 - xy + y2) = (x + y)(x2 - xy + y2) + 2(x2 - xy + y2) = (x2 - xy + y2)(x + y + 2)
e) = x4 - x3 - x3 + x2 - x2 + x + x - 1 = x3(x - 1) - x2(x - 1) - x(x - 1) + x - 1 = (x - 1)(x3 - x2 - x + 1) = (x - 1)(x - 1)(x2 - 1) = (x - 1)3(x + 1)
f) = x3 - 3x2 - x2 + 3x + 9x - 27 = x2(x - 3) - x(x - 3) + 9(x - 3) = (x-3)(x2 - x + 9)
g) chắc là 3xyz
= x2y + xy2 + y2z + yz2 + x2z + xz2 + 3xyz = x2y + xy2 + xyz + y2z + yz2 + xyz + x2z + xz2 + xyz = (x + y + z)(xy + yz + xz)
h) = 23 -(3x)3 = (2 - 3x)(4 + 6x + 9x2)
i) = (x + y - x + y)(x + y + x - y) = 2y*2x = 4xy
k) = (x3 - y3)(x3 + y3) = (x - y)(x2 + xy +y2)(x + y)(x2 - xy +y2).
c, =(5x)^3 + (y^2)^ 3 = (5x+y^2)(25x^2 - 5xy^2 + y^4)
d, = (0,5.(a+1))^3-1^3 = ( 0,5(a+1) - 1 ) ( 0,25(a+1) ^2 +a,5(a+1) + 1)
e,2x( x+ 1 ) + 2(x+ 1 ) = 2(x+1)(x+1) = 2(x+1)^2
g, y^2 (x^2 + y) - zx^2 - zy = x^2.y^2 - z.x^2 + y^3 - zy = x^2 (y^2 - z) + y (y^2 -z) = (x^2 +y) (y^2 -z)
h,4.x(x-2y) + 8.y(2y -x) = 4x( x- 2 y ) -8 (x - 2y) = (4x - 8) (x-2y)=4(x-2)(x-2y)
k,=(x+1)(3x(x+1)-5x+7) =(x+1) (3x^2 +3x - 5x + 7)
a) Ta có: \(4\left(2-x\right)^2+xy-2y\)
\(=4\left(x-2\right)^2+y\left(x-2\right)\)
\(=\left(x-2\right)\left[4\left(x-2\right)+y\right]\)
\(=\left(x-2\right)\left(4x-8+y\right)\)
b) Ta có: \(3a^2x-3a^2y+abx-aby\)
\(=3a^2\left(x-y\right)+ab\left(x-y\right)\)
\(=\left(x-y\right)\left(3a^2+ab\right)\)
\(=a\left(x-y\right)\left(3a+b\right)\)
c) Ta có: \(x\left(x-y\right)^3-y\left(y-x\right)^2-y^2\left(x-y\right)\)
\(=x\left(x-y\right)^3-y\left(x-y\right)^2-y^2\left(x-y\right)\)
\(=\left(x-y\right)\left[x\left(x-y\right)^2-y\left(x-y\right)-y^2\right]\)
\(=\left(x-y\right)\left[x\left(x^2-2xy+y^2\right)-yx+y^2-y^2\right]\)
\(=\left(x-y\right)\left(x^3-2x^2y+xy^2-xy\right)\)
d) Ta có: \(2ax^3+6ax^2+6ax+18a\)
\(=2ax^2\left(x+3\right)+6a\left(x+3\right)\)
\(=\left(x+3\right)\left(2ax^3+6a\right)\)
\(=2a\left(x+3\right)\left(x^3+3\right)\)
e) Ta có: \(x^2y-xy^2-3x+3y\)
\(=xy\left(x-y\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(xy-3\right)\)
h) \(=3x\left(2y-3z\right)\left[x^2-5\left(2y-3z\right)\right]=3x\left(2y-3z\right)\left(x^2-10y+15z\right)\)
k) \(=\left(x+2\right)\left(3x-5\right)\)
l) \(=\left(18^2+3\right)\left(x+3\right)=327\left(x+3\right)\)
m) \(=7xy\left(2x-3y+4xy\right)\)
n) \(=2\left(x-y\right)\left(5x-4y\right)\)