F.2 Math急 15points! 3Questions

(1) (m+n)n^3 - (n+m)m^3
= (n+m)(n^3 - m^3)
= (n+m)(n-m)(n^2+nm+m^2)

(2) 125y^2 + (x-5)^3y^2
= y^2 [ 5^3 + (x-5)^3 ]
= y^2 [ 5 + (x-5) ] [ 5^2 - 5(x-5) + (x-5)^2 ]
= xy^2 ( 25 - 5x + 25 + x^2 - 10x + 25 )
= xy^2 (x^2 -15x +75)

(3) 2(5r-2)^3+128
= 2 [ (5r-2)^3 + 4^3 ]
= 2 [ (5r-2) + 4 ] [ (5r-2)^2 - (5r-2)(4) + 4^2]
= 2 (5r+2) ( 25r^2 - 20r + 4 - 20r + 8 + 16)
= 2 (5r-2) ( 25r^2 - 40r +28 )

其實以上3題都用左兩條式
a^3 + b^3 = (a+b)(a^2 - ab + b^2)
a^3 - b^3 = (a-b) (a^2 + ab + b^2)

呢兩條式要勤記的,希望幫到你 :)