因式分解 唔識計

a)–343 – 8 y3
= - ( 73 + ( 2y )3 )
= - ( 7 + 2y )( 49 – 14y + 4y2 )
b)( 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 + 4x2 - 8xy + 4y2 )
= ( - x + 3y )( 7x2 – 6xy + 3y2 )
= - ( x – 3y )( 7x2 – 6xy + 3y2 )
c)2x2 + 3xy + y2
= ( 2x + y )( x + y )
d)3p2 - 7pq - 6q2
= ( 3p + 2q )( p – 3q )
e)5a2 + 7ab + 2b2
= ( 5a + b )( a + 2b )
f)4c2 + 4cd - 24d2
= 4 ( c2 + cd – 6d2 )
= 4 ( c – 2d )( c + 3d )
a,b : 用 a3 + b3 = ( a + b )( a2 – ab + b2 ) 和 a3 – b3 = ( a – b )( a2 + ab + b2 )
c,d,e,f : 用十字相乘法

a. -(343+8y^3)
=-[7^3+(2y)^3]
=-(7+2y)(49-14y+4y)
b. (x+y)^3-8(x-y)^3
=(x+y)[(x+y)^2-(x+y)^2]
=(x+y)^3 (x-y)
c. 2x^2+3xy+y^2
=(2x+y)(x+y)
d. 3p^2-7pq-6q^2
=(3p+2q)(p-3q)
e. 5a^2+7ab+2b^2
=(5a+b)(a+2b)
f. 4c^2+4cd-24d^2
=4(c^2+cd-6d2)
=4(c-2d)(c+3d)