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6) \(9x^3y^2+3x^2y^2=3x^2y^2\left(3x+1\right)\)
7) \(x^3+2x^2+3x=x\left(x^2+2x+3\right)\)
8) \(6x^2y+4xy^2+2xy=2xy\left(3x+2y+1\right)\)
9) \(5x^2\left(x-2y\right)-15x\left(x-2y\right)=5x\left(x-2y\right)\left(x-3\right)\)
10) \(3\left(x-y\right)-5x\left(y-x\right)=\left(x-y\right)\left(3+5x\right)\)
6) 9x3y2 + 3x2y2 = 3x2y2( 3x + 1 )
7) x3 + 2x2 + 3x = x( x2 + 2x + 3 )
8) 6x2y + 4xy2 + 2xy = 2xy( 3x + 2y + 1 )
9) 5x2( x - 2y ) - 15x( x - 2y ) = 5x( x - 2y )( x - 3 )
10 3( x - y ) - 5x( y - x ) = 3( x - y ) + 5x( x - y ) = ( x - y )( 3 + 5x )
1.
\(\frac{25x^4y^3-15x^3y^5+20x^2y^4}{5x^2y^3}\)
\(=\frac{5x^2y^3\left(5x^2-3xy^2+4y\right)}{5x^2y^3}\)
\(=5x^2-3xy^2+4y\)
2.
a) \(27x^4-8x=x\left(27x^3-8\right)\)
\(=x\left(3x-2\right)\left(9x^2+6x+4\right)\)
b) \(16x^2y-4xy^2-4x^3+x^2y\)
\(=4xy\left(4x-y\right)-x^2\left(4x-y\right)\)
\(=x\left(4x-y\right)\left(4y-x\right)\)
c) \(x^2-2x-5+2\sqrt{5}\)
\(=\left(x-1\right)^2-6+2\sqrt{5}\)
\(=\left(x-1\right)^2-\left(6-2\sqrt{5}\right)=\left(x-1\right)^2-\left(\sqrt{5}-1\right)^2\)
\(=\left(x-\sqrt{5}\right)\left(x-2+\sqrt{5}\right)\)
Bài 1:
\(\left(25x^4y^3-15x^3y^5+20x^2y^4\right):\left(5x^2y^3\right)\)
\(=\frac{25x^4y^3-15x^3y^5+20x^2y^4}{5x^2y^3}\)
\(=\frac{5x^2y^3\left(5x^2-3xy^2+4y\right)}{5x^2y^3}\)
\(=5x^2-3xy^2+4y\)
Bài 2:
a) \(27x^4-8x\)
\(=x\left(3x-2\right)\left(3^2x^2+2.3x+2^2\right)\)
\(=x\left(3x-2\right)\left(9x^2+6x+4\right)\)
b) \(16x^2y-4xy^2-4x^3+x^2y\)
\(=4y^2+x^2-\left(4x^2\right)^2\)
\(=x\left(-4x^2+xy+4y^2\right)\)
\(1.5x^2y^4-10x^4y^2+5x^2y^2=5x^2y^2\left(y^2-2x^2+1\right)\)
\(2.3a\left(x+y\right)-6ab\left(x+y\right)=3a\left(x+y\right)\left(1-2b\right)\)
\(3.2a^2\left(x-y\right)-4a\left(y-x\right)=2a^2\left(x-y\right)+4a\left(x-y\right)=2a\left(x-y\right)\left(a+2\right)\)
\(4.7a\left(x-2y\right)-14a^2\left(2y-x\right)=7a\left(x-2y\right)+14a^2\left(x-2y\right)=7a\left(x-2y\right)\left(2a+1\right)\)
\(a,14x^2y-21xy^2+28x^2y^2=7xy\left(x-3y+4xy\right)\\ b,x\left(x+y\right)-5x-5y=x\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-5\right)\\ c,10x\left(x-y\right)-8\left(y-x\right)=10x\left(x-y\right)+8\left(x-y\right)=\left(x-y\right)\left(10x+8\right)=2\left(x-y\right)\left(5x+4\right)\)
\(d,\left(3x+1\right)^2-\left(x+1\right)^2=\left(3x+1-x-1\right)\left(3x+1+x+1\right)=2x\left(4x+2\right)=4x\left(2x+1\right)\)\(e,x^3+y^3+z^3-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)+3xyz-3xyz=\left(x+y+z\right)\left(x^2+y^2+z^2-xy-yz-zx\right)\)
a: =-1/5x^5y^2
b: =-9/7xy^3
c: =7/12xy^2z
d: =2x^4
e: =3/4x^5y
f: =11x^2y^5+x^6
\(a,10.a^6+20a^5=10a^5\left(a+2\right)\)
\(b,5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)=5\left(x-y\right)^2\)
\(c,3ab^3+6ab^2-18ab=3ab\left(b^2+2b-1\right)\)
\(d,15x^3y^2+10x^2y^2-20x^2y^3=5x^2y^2\left(3x+2-4y\right)\)
\(e,a^2\left(x-1\right)-b\left(1-x\right)=a^2\left(x-1\right)+b\left(x-1\right)=\left(x-1\right)\left(a^2+b\right)\)
\(f,x\left(x-5\right)-4\left(5-x\right)=x\left(x-5\right)+4\left(x-5\right)=\left(x-5\right)\left(x+4\right)\)
(mk sửa lại thứ tự là a,b,c,d,e,f nha)
chúc bn học tốt
\(1,10a^6+20a^5=10a^5\left(a+10\right)\)
\(2,5x^2-10xy+5y^2=5\left(x^2-2xy+y^2\right)\)
\(=5\left(x-y\right)^2\)
\(3,3ab^3+6ab^2-18ab\)
\(=3ab\left(b^2+2b-6\right)\)
\(4,15x^3y^2+10x^2y^2-20x^2y^3\)
\(=5x^2y^2\left(3x+2-4y\right)\)
\(5,a^2\left(x-1\right)-b\left(1-x\right)\)
\(=a^2\left(x-1\right)+b\left(x-1\right)\)
\(=\left(x-1\right)\left(a^2+b\right)\)
\(6,x\left(x-5\right)-4\left(5-x\right)\)
\(=x\left(x-5\right)+4\left(x-5\right)\)
\(=\left(x+4\right)\left(x-5\right)\)