因式分解!!!!

1a) 512 - a3
= 83 – a3
= ( 8 – a )( 64 + 8a + a2 ) {因 a3 – b3 = ( a – b )( a2 + ab + b2 )}
b) 9x2 - 42xy + 49y2
= ( 3x )2 – 2 ( 3x )( 7y ) + ( 7y )2
= ( 3x – 7y )2 {因 ( a – b )2 = a2 – 2ab + b2 }
c) ( 2x – 1 )2 – 25
= ( 2x – 1 )2 - 52
= { ( 2x – 1 ) + 5 }{ ( 2x – 1 ) – 5 } {因( a + b )( a – b ) = a2 – b2 }
= ( 2x – 1 + 5 )( 2x – 1 – 5 )
= ( 2x + 4 )( 2x – 6 )
= 2 ( x + 2 ) 2 ( x – 3 )
= 4 ( x + 2 )( x – 3 )
d) 50 - 8y2
= 2 ( 25 – 4y2 )
= 2 { 52 – ( 2y )2 }
= 2 ( 5 + 2y )( 5 – 2y )
e) 8x2 - 38x + 35
= ( 4x – 5 )( 2x – 7 ) {十字相乘法}
f) 20 - 7x - 6x2
= - ( 6x2 + 7x – 20 )
= - ( 2x + 5 )( 3x – 4 )
g) - 343 - 8y3
= - {73 + ( 2y )3 }
= - ( 7 + 2y )( 49 – 14y + 4y2 ) {因a3 + b3 = ( a + b )( a2 – ab + b2 )
h) ( x + y )3 – 8 ( x – y )3
= ( x + y )3 – { 2 ( x – y ) }3
= { ( x + y ) - 2 ( x – y ) }{ ( x + y )2 + 2 ( x + y )( x – y ) + 4 ( x – y )2 }
= ( x + y – 2x + 2y )( x2 + 2xy + y2 + 2x2 – 2y2 + 4 ( x2 – 2xy + y2 ))
= ( - x + 3y )( x2 + 2xy + y2 + 2x2 – 2y2 + 4x2 – 8xy + 4y2 )
= ( - x + 3y )( 7x2 – 6xy + 3y2 )
= - ( x – 3y )( 7x2 – 6xy + 3y2 )

a^2-b^2=(a+b)(a-b)
a^3-b^3=(a-b)(a^2+ab+b^2)
用來用去二個等式
自己試試!