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1, x2+3xy+2y2= x2+xy+2xy+2y2=x(x+y)+2y(x+y)=(x+2y)(x+y)
2, x(x+2)(x+3)(x+5)+9=x(x+5)(x+2)(x+3)+9=(x2+5x)(x2+5x+6)+9
Đặt x2+5x=t, ta có
t(t+6)+9=t2+6t+9=(t+3)2=(x2+5x+3)2=(x2+8)2
3, x2+2xy+y2+2x+2y-15=(x+y)2+2(x+y)-15=(x+y)2+2(x+y)+1-16=(x+y+1)2-42
= (x+y+1-4)(x+y+1+4)=(x+y-3)(x+y+5)
4, 4x4y4+1=4x4y4+4x2y2+1-4x2y2=(2x2y2+1)2-(2xy)2=(2x2y2+1-2xy)(2x2y2+1+2xy)
a) 4(x2-y2)-8(x-ay)-4(a2-1)
=> 4x2-4y2-8x+8ay-4a2+4
=> 4(x2-y2-2x+2ay-a2+1)
c) a5+a4+a3 +a2 +a+1
=> a(a4+a3+a2+a+1)+1
a) \(x+x^2-x^3-x^4=x\left(1+x-x^2-x^3\right)\)
b) \(\left(x+1\right)^2-x-1=\left(x+1\right)^2-\left(x+1\right)=\left(x+1\right)\left(x+1-1\right)=x\left(x+1\right)\)
c) \(x^2-2x+1-y^2+2y-1=\left(x-1\right)^2-\left(y-1\right)^2=\left(x-1+y-1\right)\left(x-1-y+1\right)\)
\(=\left(x+y-2\right)\left(x-y\right)\)
d) \(3xy-z-3x+yz=3x\left(y-1\right)-x\left(y-1\right)=2x\left(y-1\right)\)
e) \(x^4-1-3\left(x^2+1\right)=\left(x^2-1\right)\left(x^2+1\right)-3\left(x^2+1\right)=\left(x^2+1\right)\left(x^2-1-3\right)\)
\(=\left(x^2+1\right)\left(x^2-4\right)=\left(x^2+1\right)\left(x-2\right)\left(x+2\right)\)
a, \(x+x^2-x^3-x^4=-x\left(x+1\right)^2\left(x-1\right)\)
b, \(\left(x+1\right)^2-x-1=x^2+2x+1-x-1=x^2+x=x\left(x+1\right)\)
c, \(x^2-2x+1-y^2+2y-1=\left(x-1\right)^2-\left(y-1\right)^2\)để thế này đc thôi
d, \(3xy-z-3x+yz=2x\left(y-1\right)\)
e, \(x^4-1-3\left(x^2+1\right)=x^4-1-3x^2-4=\left(x^2+1\right)\left(x-2\right)\left(x+2\right)\)
1 ) \(a\left(m+n\right)+b\left(m+n\right)\)
\(=\left(a+b\right)\left(m+n\right)\)
2 ) \(a^2\left(x+y\right)-b^2\left(x+y\right)\)
\(=\left(a^2-b^2\right)\left(x+y\right)\)
\(=\left[\left(a-b\right).\left(a+3\right)\right]\left(x+y\right)\)
3 ) \(6a^2-3a+12ab\)
\(=3a.2a-3a+3a.4b\)
\(=3a.\left(2a-1+4b\right)\)
4 ) \(2x^2y^4-2x^4y^2+6x^3y^3\)
\(=2x^2y^2.y^2-2x^2y^2.x^2+2x^2y^2.3xy\)
\(=2x^2y^2\left(y^2-x^2+3xy\right)\)
5 ) \(\left(x+y\right)^3-x\left(x+y\right)^2\)
\(=\left(x+y\right)^2.\left(x+y-x\right)\)
\(=\left(x+y\right)^2.y\)
1)a(m+n)+b(m+n)
=(a+b)(m+n)
2)a2(x+y)-b2(x+y)
=(a2-b2)(x+y)
3)6a2-3a+12ab
=3a.2a-3a.(1-4b)
=3a.(2a-1+4b)
5)(x+y)3-x(x+y)2
=(x+y)(x+y)2-x(x+y)2
=(x+y)2(x+y-x)