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a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
a) \(x^2-y^2-5x-5y\)
\(=\left(x^2-y^2\right)-\left(5x+5y\right)\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-5\right)\)
b) \(5x^3-5x^2y-10x^2+10xy\)
\(=\left(5x^3-5x^2y\right)-\left(10x^2-10xy\right)\)
\(=5x^2\left(x-y\right)-10x\left(x-y\right)\)
\(=\left(x-y\right)\left(5x^2-10x\right)\)
\(=5x\left(x-y\right)\left(x-2\right)\)
c) \(x^3-2x^2-x+2\)
\(=\left(x^3-2x^2\right)-\left(x-2\right)\)
\(=x^2\left(x-2\right)-\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2-1\right)\)
\(=\left(x-2\right)\left(x-1\right)\left(x+1\right)\)
d) \(-y^2+2xy-x^2+3x-3y\)
\(=-\left(y^2-2xy+x^2\right)+\left(3x-3y\right)\)
\(=-\left(y-x\right)^2+3\left(x-y\right)\)
\(=-\left(x-y\right)^2+3\left(x-y\right)\)
\(=\left(x-y\right)\left[-\left(x-y\right)+3\right]\)
\(=\left(x-y\right)\left(-x+y+3\right)\)
g) \(4x^2-8x+3\)
\(=4x^2-6x-2x+3\)
\(=\left(4x^2-6x\right)-\left(2x-3\right)\)
\(=2x\left(2x-3\right)-\left(2x-3\right)\)
\(=\left(2x-3\right)\left(2x-1\right)\)
h) \(2x^2-5x-7\)
\(=2x^2+2x-7x-7\)
\(=\left(2x^2+2x\right)-\left(7x+7\right)\)
\(=2x\left(x+1\right)-7\left(x+1\right)\)
\(=\left(x+1\right)\left(2x-7\right)\)
k) \(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left[\left(x^2\right)^2+2.x^2.2+2^2\right]-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
a,x2-z2+y2-2xy
=(x2-2xy+y2)-z2
=(x-y)2-z2
b,-x-y2+x2-y
=(x2-y2)-(x+y)
=(x-y)(x+y)-(x+y)
=(x+y)(x-y-1)
c,x2-2xy-4z2+y2
=(x2-2xy+y2)-(2z)2
=(x-y)2-(2z)2
=(x-y-2z)(x-y+2z)
d,x(x+y)-5x-5y
=x(x+y)-5(x+y)
=(x+y)(x-5)
e, x2 - 5x + 5y - y2
=(x2-y2)-5(x-y)
=(x+y)(x-y)-5(x+y)
=(x+y)(x-y-5)
f, x2 + 4x + 3
=x2+x+3x+3
=x(x+1)+3(x+1)
=(x+1)(x+3)
g, 10x ( x - y) - 8 (y - x)
=10x(x-y)+8(x-y)
=2(x-y)(5x+4)
h, x2 - 3x + 2
=x2-x-2x+2
=x(x+1)-2(x-1)
=(x+1)(x-2)
a,3x3-x2-21x+7
=(3x3-x2)-(21x-7)
=x2(3x-1)-7(3x-1)
=(3x-1)(x2-7)
b,x3-4x2+8x-8
=(x3-8)-(4x2-8x)
=(x-2)(x2+2x+4)-4x(x-2)
=(x-2)(x2+2x-4x+4)
=(x-2)(x2-2x+4)
c,x3-5x2-5x+1
=(x3+1)-(5x2+5x)
=(x+1)(x2-x+1)-5x(x+1)
=(x+1)(x2-x-5x+1)
=(x+1)(x2-6x+1)
d,x2y-xz+z-y
=(x2y-y)-(xz-z)
=y(x2-1)-z(x-1)
=y(x+1)(x-1)-z(x-1)
=(x-1)(x+y-z+1)
e,x4-x3-x2-1
=(x4-x2)-(x3+1)
=x2(x2-1)-(x+1)(x2-x+1)
=x2(x-1)(x+1)-(x+1)(x2-x+1)
=(x+1)(x2+x-1-x2+x-1)
=(x+1)(2x-2)
=2(x+1)(x-1)
1) \(x^2-x-y^2-y=\left(x^2-y^2\right)-\left(x+y\right)=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\)
\(x^2-2xy+y^2-z^2=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)
2)\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(a+5\right)\)
\(a^3-a^2x-ay+xy=a^2\left(a-x\right)-y\left(a-x\right)=\left(a-x\right)\left(a^2-y\right)\)
c) \(x^2+x-ax-a\)
\(=x\left(x+1\right)-a\left(x+1\right)\)
\(=\left(x+1\right)\left(x-a\right)\)
d) \(2xy-ax+x^2-2ay\)
\(=2y\left(x-a\right)+x\left(x-a\right)\)
\(=\left(x-a\right)\left(2y+x\right)\)
e) \(x^2y+xy^2-x-y\)
\(=xy\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(xy-1\right)\)
f) \(25-10x-4y^2+x^2\)
\(=\left(x^2-10x+25\right)-\left(2y\right)^2\)
\(=\left(x-5\right)^2-\left(2y\right)^2\)
\(=\left(x-5-2y\right)\left(x-5+2y\right)\)
g) \(x^3-6xy+9y^2-36\)
h) \(4x^2-9y^2+4x-6y\)
\(=\left(2x\right)^2-\left(3y\right)^2+2\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y\right)+2\left(2x-3y\right)\)
\(=\left(2x-3y\right)\left(2x+3y+2\right)\)
k) \(-x^2+5x+2xy-5y-y^2\)
\(=-\left(x^2-2xy+y^2\right)+5\left(x-y\right)\)
\(=-\left(x-y\right)^2+5\left(x-y\right)\)
\(=\left(x-y\right)\left(-x+y+5\right)\)
i) \(4x^2-25y^2-6x+15y\)
\(=\left(2x\right)^2-\left(5y\right)^2-3\left(2x-5y\right)\)
\(=\left(2x-5y\right)\left(2x+5y\right)-3\left(2x-5y\right)\)
\(=\left(2x-5y\right)\left(2x+5y-3\right)\)
a, \(x\left(y+z\right)^2+y\left(x+z\right)^2+z\left(x+y\right)^2+4xyz\)
\(=x\left(y+z\right)^2+x^2\left(y+z\right)+yz\left(y+z\right)\)
\(=\left(y+z\right)\left(xy+xz+z^2+yz\right)\)
\(=\left(y+z\right)\left[x\left(x+y\right)+z\left(x+y\right)\right]\)
\(=\left(y+z\right)\left(x+z\right)\left(x+y\right)\)
b, \(yz\left(y+z\right)+xz\left(z-x\right)-xy\left(x+y\right)\)
\(=yz\left(y+z\right)+xz^2-x^2z-x^2y-xy^2\)
\(=yz\left(y+z\right)-x\left(y+z\right)\left(y-z\right)-x^2\left(y+z\right)\)
\(=\left(y+z\right)\left(yz-xy+xz-x^2\right)\)
\(=\left(y+z\right)\left[y\left(z-x\right)+x\left(z-x\right)\right]\)
\(=\left(y+z\right)\left(y+x\right)\left(z-x\right)\)
\(x^2-y^2-5x-5y\)
\(=\left(x-y\right)\left(x+y\right)-5\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-5\right)\)
học tốt
a, 5x2 - 45x = 5x(x - 9)
b, 3x3y - 6x2y - 3xy3 - 6axy2 - 3a2xy + 3xy
= 3xy(x2 - 2x - y2 - 2ay - a2 + 1)
= 3xy[ (x2 - 2x + 1) - (a2 + 2ay + y2) ]
= 3xy[ (x - 1)2 - (a + y)2 ]
= 3xy(x - 1 + a + y)(x - 1 - a - y)
f, 3xy2 - 12xy + 12x
= 3x(y2 - 4y + 4)
= 3x(y - 2)2
g, 2x2 - 8x + 8
= 2(x2 - 4x + 4)
= 2(x - 2)2
h, 5x3 + 10x2y + 5xy2
= 5x( x2 + 2xy + y2 )
= 5x(x + y)2
k, x2 + 4x - 2xy - 4y + y2
= (x2 - 2xy + y2) + (4x - 4y)
= (x - y)2 + 4(x - y)
= (x - y)(x - y + 4)
i, x3 + ax2 - 4a - 4x
= (x3 - 4x) + (ax2 - 4a)
= x(x2 - 4) + a(x2 - 4)
= (x + a)(x2 - 4)
= (x + a)(x + 2)(x - 2)
Chúc bạn học tốt !
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a: \(x^2-y^2-x-y\)
\(=\left(x-y\right)\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x-y-1\right)\)
f: \(x^3-5x^2-5x+1\)
\(=\left(x+1\right)\left(x^2-x+1\right)-5x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-6x+1\right)\)