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a) x2 - y2 + 4x + 4
= ( x2 + 4x + 4 ) - y2
= ( x + 2 )2 - y2
= ( x + 2 - y )( x + 2 + y )
b) x2 - 2xy + y2 - 1
= ( x2 - 2xy + y2 ) - 1
= ( x - y )2 - 12
= ( x - y - 1 )( x - y + 1 )
c) x2 - 2xy + y2 - 4
= ( x2 - 2xy + y2 ) - 4
= ( x - y )2 - 22
= ( x - y - 2 )( x - y + 2 )
d) x2 - 2xy + y2 - z2
= ( x2 - 2xy + y2 ) - z2
= ( x - y )2 - z2
= ( x - y - z )( x - y + z )
e) 25 - x2 + 4xy - 4y2
= 25 - ( x2 - 4xy + 4y2 )
= 52 - ( x - 2y )2
= ( 5 - x + 2y )( 5 + x - 2y )
f) x2 + y2 - 2xy - 4z2
= ( x2 - 2xy + y2 ) - 4z2
= ( x - y )2 - ( 2z )2
= ( x - y - 2z )( x - y + 2z )
a) x^4 - x^3 - x + 1
= x^3 ( x - 1 ) - ( x- 1 )
= ( x^3 - 1 )(x - 1)
= ( x- 1 )^2 (x^2 + x + 1 )
a)x4-x3-x+1
=x3(x-1)-(x-1)
=(x-1)(x3-1)
=(x-1)(x-1)(x2+x+1)
=(x-1)2(x2+x+1)
b)5x2-4x+20xy-8y
(sai đề)
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)\(5x-5y+ax-ay=5\left(x-y\right)+a\left(x-y\right)=\left(x-y\right)\left(a+5\right)\)
\(a^3-a^2x-ay+xy=a^2\left(a-x\right)-y\left(a-x\right)=\left(a-x\right)\left(a^2-y\right)\)
x6+3x4y2-8x3y3+3x2y4+y6= x6+3x4y2+3x2y4+y6-8x3y3=(x2+y2)3-(2xy)3
= (x2+y2-2xy)[(x2+y2)2+2xy(x2+y2)+(2xy)2]= (x-y)2(x4+6x2y2+y4+2x3y+2xy3)
(x2+y2-5)2-4x2y2-16xy-16=(x2+y2-5)2-(4x2y2+16xy+16)=(x2+y2-5)2-(2xy+4)2
=(x2+y2-5+2xy+4)(x2+y2-5-2xy-4)=(x2+2xy+y2-1)(x2-2xy+y2-9)=[(x+y)2-1][(x-y)2-32]=(x+y-1)(x+y+1)(x-y-3)(x-y+3)
x4+324=x4+36x2+324-36x2=(x2+18)2-(6x)2=(x2+18-6x)(x2+18+6x)
a) \(x^6-y^6=\left(x^3\right)^2-\left(y^3\right)^2\)
\(=\left(x^3+y^3\right)\left(x^3-y^3\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)\)
b) sửa đề nhé!
\(6x-9-x^2=-\left(x^2-6x+9\right)\)
\(=-\left(x-3\right)^2\)
1, x2(x2+2x+1)=x2(x+1)2
2, 2(x2+2x+1-y2)=2(x+1-y)(x+1+y)
3, 16-(x2+2xy+y2)=(4-x-y)(4+x+y)
\(x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
hk tốt
^^
\(x^3-4x-12+3x^2=x\left(x^2-2^2\right)+3\left(x^2-2^2\right)=\left(x-2\right)\left(x+2\right)\left(x+3\right)\)
\(x^2+2xy-15y^2=x^2+2xy+y^2-16y^2=\left(x+y\right)^2-\left(4y\right)^2=\left(x-3y\right)\left(x+5y\right)\)
\(\left(x-y\right)^2-6\left(x-y\right)-16=\left(x-y\right)^2-2\times\left(x-y\right)\times3+9-25=\left(x-y-3\right)^2-5^2=\left(x-y-8\right)\left(x-y+2\right)\)
1/ 4x2y-y2=y(4x2-y)
3/ 1-x2-2xy-y2=1-(x2+2xy+y2)=1-(x+y)2=(1-x-y)(1+x+y)
2)
=x2-2xy+y2 - 9y2
=(x-y)2 - (3y)2
=(x-y+3y)(x-y-3y)
=(x+2y)(x-4y)
4)
=(x3+x2y)-(x2z+xyz)
=x2(x+y)-xz(z+y)
=(x+y)(x2-xz)