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\(x^8+64\)
\(=x^8+16x^4+64-16x^4\)
\(=\left(x^4\right)^2+2.x^4.8+8^2-16x^4\)
\(=\left(x^4+8\right)^2-\left(4x^2\right)^2\)
\(=\left(x^4+8-4x^2\right)\left(x^4+8+4x^2\right)\)
5x2+11x+6
=5x2+5x+6x+6
=(5x2+5x)+(6x+6)
=5x(x+1)+6(x+1)
=(x+1)(5x+6)
\(a,=xy\left(x+2y+1\right)\\ b,=x^2\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)\\ c,=x^2-5x+3x-15=\left(x-5\right)\left(x+3\right)\\ d,=\left(x-2\right)\left(x+2\right)+\left(x-2\right)^2=\left(x-2\right)\left(x+2+x-2\right)=2x\left(x-2\right)\\ e,=\left(x+1\right)^2-y^2=\left(x+y+1\right)\left(x-y+1\right)\\ g,=\left(x+9-6x\right)\left(x+9+6x\right)=\left(9-5x\right)\left(7x+9\right)\\ h,=\left(x-y\right)^2-\left(z-t\right)^2=\left(x-y-z+t\right)\left(x-y+z-t\right)\\ i,=\left(x-1\right)^3-y^3=\left(x-y-1\right)\left(x^2-2x+1+xy+y+y^2\right)\)
a: =(6x)^2-(3x-2)^2
=(6x-3x+2)(6x+3x-2)
=(9x-2)(3x+2)
d: \(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)
\(=4x\cdot\left[x^2+2x+1+x^2-2x+1\right]\)
=8x(x^2+1)
e: =(4x)^2-2*4x*3y+(3y)^2
=(4x-3y)^2
f: \(=-\left(\dfrac{1}{4}x^4-2\cdot\dfrac{1}{2}x^2\cdot2y^3+4y^6\right)\)
\(=-\left(\dfrac{1}{2}x^2-2y^3\right)^2\)
g: =(4x)^3+1^3
=(4x+1)(16x^2-4x+1)
k: =x^3(27x^3-8)
=x^3(3x-2)(9x^2+6x+4)
l: =(x^3-y^3)(x^3+y^3)
=(x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)
a: \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
b: \(4a^4-4a^2b^2+b^4=\left(2a^2-b^2\right)^2\)
\(x^6-2x^3y+y^2=\left(x^3-y\right)^2\)
b: \(\left(x+y\right)^3-\left(x-y\right)^3\)
\(=\left(x+y-x+y\right)\left(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2\right)\)
\(=2y\left(3x^2+y^2\right)\)
\(25x^4-10x^2y^2+y^4=\left(5x^2-y^2\right)^2\)
\(-a^2-2a-1=-\left(a+1\right)^2\)
Bài 1
( x - y )2 - 4
= ( x - y )2 - 22
= ( x - y - 2 )( x - y + 2 )
x2 - 16( x + y )2
= x2 - 42( x + y )2
= x2 - ( 4x + 4y )2
= ( x2 - 4x - 4y )( x2 - 4x + 4y )
8x3 + 36x2y + 54xy2 + 27y3
= ( 2x )3 + 3.( 2x )2.3y + 3.2x.( 3y )2 + ( 3y )3
= ( 2x + 3y )3
Bài 2.
a) ( x2 + 4 )( x2 - 4 ) - ( x2 + 1 )( x2 - 1 )
= [ ( x2 )2 - 42 ] - [ ( x2 )2 - 12 ]
= x4 - 16 - x4 + 1
= -15
b) ( y - 3 )( y + 3 )( y2 + 9 )( y2 + 2 )( y2 - 2 )
= [ ( y - 3 )( y + 3 )( y2 + 9 ) ][ ( y2 + 2 )( y2 - 2 ) ]
= { [ ( y - 3 )( y + 3 ) ]( y2 + 9 ) }[ ( y2 )2 - 22 ]
= [ ( y2 - 9 )( y2 + 9 ) ]( y4 - 4 )
= ( y4 - 81 )( y4 - 4 )
= y4( y4 - 4 ) - 81( y4 - 4 )
= y8 - 4y4 - 81y4 + 324
= y8 - 85y4 + 324