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a) \(a\left(x-y\right)+bx-by\)
\(=a\left(x-y\right)+b\left(x-y\right)\)
\(=\left(a-b\right)\left(x-y\right)\)
\(a,a\left(x-y\right)+bx-by\)
\(=a\left(x-y\right)+b\left(x-y\right)\)
\(=\left(a+b\right)\left(x-y\right)\)
\(b,ac+bc+a+b\)
\(=\left(a+b\right)c+\left(a+b\right)\)
\(\left(a+b\right)\left(c+1\right)\)
\(c,5x^2-5ax-7a+7x\)
\(=5x\left(x-a\right)-7\left(a-x\right)\)
\(=5x\left(x-a\right)+7\left(x-a\right)\)
\(=\left(5x+7\right)\left(x-a\right)\)
\(d,7z^2-7yz-4z+4y\)
\(=7z\left(z-y\right)-4\left(z-y\right)\)
\(=\left(7z-4\right)\left(z-y\right)\)
\(e,x^3+3x^2+3x+9\)
\(=\left(x^3+3x^2\right)+\left(3x+9\right)\)
\(=x^2\left(x+3\right)+3\left(x+3\right)\)
\(=\left(x^2+3\right)\left(x+3\right)\)
\(f,x^3-x^2y-x^2z-xyz\)
\(=\left(x^3-x^2y\right)+\left(-x^2z-xyz\right)\)
\(=x^2\left(x-y\right)-xz\left(x-y\right)\)
\(=\left(x^2-xz\right)\left(x-y\right)\)
\(=x\left(x-z\right)\left(x-y\right)\)
\(g,pq-p^2-5\left(p-q\right)\)
\(=\left(pq-p^2\right)-5\left(p-q\right)\)
\(=p\left(q-p\right)+5\left(q-p\right)\)
\(=\left(p+5\right)\left(q-p\right)\)
`a, P = 2x(3 - x^2)`
`b, Q = 5x^2(x-3y)`
`c, R = xy(3x^2y^2 - 6y^2z + 1)`
a) \(P=6x-2x^3\)
\(P=2x\left(3+x^2\right)\)
b) \(Q=5x^3-15x^2y\)
\(Q=5x^2\left(x-3y\right)\)
c) \(R=3x^3y^3-6xy^3z+xy\)
\(R=xy\left(3x^2y^2-6y^2z+1\right)\)
a, \(=\left(xy+1+x-y\right)\left(xy+1-x+y\right)\)
b, \(\left(x+y-x+y\right)[\left(x+y\right)^2+\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2]\)
\(=2y[x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2]\)
\(=2y\left(3x^2+y^2\right)\)
c,\(=3\left(x+1\right)^2\left(x^2-x+1\right)y^2\)
câu a, b áp dụng hằng đẳng thức rồi làm nha
c) 3x4y2 + 3x3y2 + 3xy2 + 3y2
= ( 3x4y2 + 3x3y2 ) + ( 3xy2 + 3y2 )
= 3x3y2 ( x + 1) + 3y2 ( x + 1 )
= ( 3x3y2 + 3y2 ) ( x + 1 )
= 3y2 ( x3 + 1 ) ( x + 1 )
= 3y2 ( x + 1 ) ( x2 - x + 1 ) ( x + 1 )
= 3y2 ( x + 1 )2 ( x2 - x + 1 )
`b)x^3+y^3+z^3-3xyz`
`=x^3+3xy(x+y)+z^3-3xy(x+y)-3xyz`
`=(x+y)^3+z^3-3xy(x+y+z)`
`=(x+y+z)[(x+y)^2-z(x+y)+z^2]-3xy(x+y)`
`=(x+y+z)(x^2+2xy+y^2-zx-yz-3xy+z^2)`
`=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)`
a.
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1+3z\right)\left[\left(x+1\right)^2+3z\left(x+1\right)+9z^2\right]\)
\(=\left(x+3z+1\right)\left(x^2+2x+1+3zx+3z+9z^2\right)\)
b.
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c.
\(=x^4-1+4x^2-4\)
\(=\left(x^2-1\right)\left(x^2+1\right)+4\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
a) Ta có: \(x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
b) Ta có: \(x^2-2xy+y^2-zx+yz\)
\(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
c) Ta có: \(x^4+4x^2-5\)
\(=x^4+4x^2+4-9\)
\(=\left(x^2+2\right)^2-3^2\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
`a, 4a^2 + 4a + 1 = (2a+1)^2`
`b, -3x^2 + 6xy - 3y^2`
` = -3(x-y)^2`
`c, (x+y)^2 - 2(x+y)z + z^2`
`= (x+y-z)^2`
a) $x^3-3x^2y+4x-12y$
$=(x^3-3x^2y)+(4x-12y)$
$=x^2(x-3y)+4(x-3y)$
$=(x-3y)(x^2+4)$
b) $4x^2-y^2+4y-4$
$=4x^2-(y^2-4y+4)$
$=(2x)^2-(y^2-2\cdot y\cdot2+2^2)$
$=(2x)^2-(y-2)^2$
$=[2x-(y-2)][2x+(y-2)]$
$=(2x-y+2)(2x+y-2)$
c) $9x^2-6x-y^2+2y$
$=(9x^2-y^2)-(6x-2y)$
$=[(3x)^2-y^2]-2(3x-y)$
$=(3x-y)(3x+y)-2(3x-y)$
$=(3x-y)(3x+y-2)$
$\text{#}Toru$
\(a,=xy\left(x+2y+1\right)\\ b,=x^2\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\\ c,=x^2-5x+3x-15=\left(x-5\right)\left(x+3\right)\\ d,=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2=\left(x-2\right)\left(x+2+x-2\right)=2x\left(x-2\right)\\ e,=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\\ g,=\left(x+9-6x\right)\left(x+9+6x\right)=\left(9-5x\right)\left(7x+9\right)\\ h,=\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\\ i,=\left(x-1\right)^3-y^3=\left(x-y-1\right)\left(x^2-2x+1+xy+y+y^2\right)\)
a, a(x-y) + bx - by = a(x - y ) +b.(x-y) = (x-y)(a-b)
b, ac+bc + a + b = c.(a+b) +(a+b) = (a+b)(c+1)
c, \(5a^2-5ax-7a+7x=5a.\left(a-x\right)-7.\left(a-x\right)=\left(a-x\right)\left(5a-7\right)\)
d, \(7z^2-7yz-4z+4y=7z.\left(z-y\right)-4.\left(z-y\right)=\left(z-y\right)\left(7z-4\right)\)
e, \(x^3+3x^2+3x+9=x^2.\left(x+3\right)+3\left(x+3\right)=\left(x+3\right)\left(x^2+3\right)\)
g, \(pq-p^2-5\left(p-q\right)=p.\left(q-p\right)+5\left(q-p\right)=\left(q-p\right)\left(p+5\right)\)