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b)x2+2xy+y2-16=(x+y)2-42=(x+y+4)(x+y-4)
c)3x2+5x-3xy-5y=x(3x+5)-y(3x+5)=(3x+5)(x-y)
d)4x2-6x3y-2x2+8x=2x(2x-3x2y-x+4)
e)x2-4-2xy+y2=(x2-2xy+y2)-4=(x-y)2-22=(x-y-2)(x-y+2)
k)x2-y2-z2-2yz=x2-(y+z)2=(x-y-z)(x+y+z)
m)6xy+5x-5y-3x2-3y2=3(x2-2xy+y2)+5(x-y)=3(x-y)2+5(x-y)=(x-y)(3x-3y+5)
1 \(=\left(4x^2+4x+1\right)-\left(3y\right)^2\)
\(=\left(2x+1\right)^2-\left(3y\right)^2\)
\(=\left(2x+1-3y\right)\left(2x+1+3y\right)\)
2,\(=\left(x^2+2xy+y^2\right)-\left(z^2-2zt+t^2\right)\)
\(=\left(x+y\right)^2-\left(z-t\right)^2\)
\(=\left(x+y+z-t\right)\left(x+y-z+t\right)\)
3,\(=9x\left(x-y\right)-7\left(x-y\right)\)
\(=\left(x-y\right)\left(9x-7\right)\)
4\(=3\left(x-y\right)+a\left(x-y\right)\)
\(=\left(x-y\right)\left(3+a\right)\)
4x(x+y)(x+y+z)(x+z)+(yz)^2
=(2x(x+y+z))(2(x+y)(x+z)+(yz)^2
=(2x^2+2xy+2xz)(2x^2+2xy+2xz+2yz)+(yz)^2
Đặt t=C
=(t-yz)(t+yz)-(yz)^2
=t^2-(yz)^2+(yz)^2=t^2=(2x^2+2xy+2xz+yz)^2
=
a ) = 3 ( x^2 + 2xy + y^2 - z^2 )
= 3 [ ( x + y)^2 - z^2]
= 3 ( x + y - z)( x + y + z)
b) 4 y^ 2 - 5 y - 6 = 4y^2 - 8y + 3y - 6 = 4y ( y- 2 ) + 3 ( y- 2 ) = ( 4y +3 )( y - 2 )
d) x^4 + x^2y^2 + y^4 = x^4 + 2 x^2y^2 + y^4 - x^2y^2 = ( x^2 + y^2 )^2 - (xy)^2 = ( x^2 - xy + y^ 2)( x^2 + xy + y^2)
a: \(=x\left[49-x^2\left(2x+1\right)^2\right]\)
\(=x\left[49-\left(2x^2+x\right)^2\right]\)
\(=x\left[\left(7-2x^2-x\right)\left(7+2x^2+x\right)\right]\)
b: \(=5\left[25x^2-\left(y^2-4y+4\right)\right]\)
\(=5\left[\left(5x-y+2\right)\left(5x+y-2\right)\right]\)
c: \(=1-4x^2-x\left(x^2-4\right)\)
\(=1-4x^2-x^3+4x\)
\(=\left(1-x\right)\left(1+x+x^2\right)-4x\left(x-1\right)\)
\(=\left(1-x\right)\left(1+x+x^2+4x\right)\)
\(=\left(1-x\right)\left(x^2+5x+1\right)\)
e: =(x-9)(x+6)
a) x2-x-y2-y=(x2-y2)-(x+y)=(x+y)(x-y)-(x+y)=(x+y)(x-y-1)
b)x2-2xy+y2-z2=(x-y)2-z2=(x-y-z)(x-y+z)
c)5x-5y+ax-ay=5(x-y)+a(x-y)=(x-y)(5+a)
d)a3-a2x-ay+xy=a2(a-x)-y(a-x)=(a-x)(a2-y)
e)4x2-y2+4x+1=[(2x)2+2.2x.1+12]-y2=(2x+1)2-y2=(2x+1-y)(2x+1+y)
Chúc bạn học tốt!
1) \(5x-5y+x\left(x-y\right)\)
\(=5\left(x-y\right)+x\left(x-y\right)\)
\(=\left(x-y\right)\left(x+5\right)\)
2) \(x^2+4x+3\)
\(=\left(x^2+x\right)+\left(3x+3\right)\)
\(=x\left(x+1\right)+3\left(x+1\right)\)
\(=\left(x+1\right)\left(x+3\right)\)
3) \(x^2-2xy+y^2-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
4) \(x\left(x-5\right)-3x+15\)
\(=x\left(x-5\right)-3\left(x-5\right)\)
\(=\left(x-5\right)\left(x-3\right)\)
5) \(y^2-x^2+2x-1\)
\(=y^2-\left(x^2-2x+1\right)\)
\(=y^2-\left(x-1\right)^2\)
\(=\left(x+y-1\right)\left(y-x+1\right)\)
\(1.\left(x-y\right)\left(x+5\right)\)
\(2.\left(x+1\right)\left(x+3\right)\)
\(3.\left(x-y-z\right)\left(x-y+z\right)\)
\(4.\left(x-3\right)\left(x-5\right)\)
\(5.\left(y-x+1\right)\left(y+x+1\right)\)
\(7.\left(x+1\right)\left(x-2\right)^2\)
\(8.\left(x-5\right)\left(x+3\right)\)
\(10.\left(y+1\right)\left(2x+z\right)\)