Factorize (急問)

1)
Expand and get
27a^2 + 54ab + 27b^2 + 72a^2 - 72b^2 + 48a^2 - 96ab + 48b^2
= 147a^2 + 6ab + 3b^2
= 3(49a^2 + 2ab + b^2)

2)
Simply add them up and get
65(x + 1)^3

2. ) 64(x+1)^3 + (x+1)^3
=(64+1)(x+1)^3
=65(x+1)^3

2007-11-10 23:25:10 補充：
1. ) 27(a+b)^2 + 72a^2 - 72b^2 + 48(a-b)^2 =27(a+b)^2+72(a+b)(a- b)+48(a-b)^2=3[3^2(a+b)^2+2*3*4(a+b)(a- b)+4^2(a-b)^2]=3(3a+3b+2a-2b)^2=3(5a- b)^2

2007-11-10 23:30:34 補充：
sorry, 1 should be 1. ) 27(a+b)^2 + 72a^2 - 72b^2 + 48(a-b)^2 =27(a+b)^2+72(a+b)(a- b)+48(a-b)^2=3[3^2(a+b)^2+2*3*4(a+b)(a- b)+4^2(a-b)^2]=3(3a+3b+4a-4b)^2=3(7a - b)^2