f.2 (5a-7)^3+125---------------------------因式分解

(5a-7)^3+125
=(5a-7)^3+5^3
=(5a-7+5)[(5a-7)^2-5(5a-7)+5^2]
=(5a-2)(25a^2-70a+49-25a+35+25)
=(5a-2)(25a^2-95a+109)//

2007-09-07 18:04:21 補充：
(a+b)^3+(2a-b)^3 =(a+b+2a-b)[(a+b)^2-2(a+b)(2a-b)+(2a-b)^2]=3a(a^2+2ab+b^2-4a^2-4ab-4ab+4b^2+4a^2-4ab+b^2)=3a(a^2-10ab+6b^2)//

1. (5a-7)^3+125
=(5a-7)^3+5^3
=(5a-7+5)[(5a-7)^2-5(5a-7)+25)
=(5a-2)(25a^2 -70a+49-25a-35+25)
=(5a-2)(25a^2 -95a+39)
2. (a+b)^3+(2a-b)^3
=(a+b+2a-b)[(a+b)^2 -(a+b)(2a-b)+(2a-b)^2]
=(3a)(a^2 +2ab+b^2 -a(2a-b)+b(2a-b)+4a^2 -4ab+b^2)
=3a(a^2 +2ab+b^2 -2a^2 +ab+2ab-b^2 +4a^2 -4ab+b^2
=3a(3a^2 +ab+b^2)

[ngaichuens] answer of Q2 is wrong!
The questions make use of the formula (x³ + y³) = (x + y)(x² - xy + y²)
1.
(5a-7)³+125
= (5a-7)³ + 5³
= [(5a-7) + 5] [(5a-7)² - (5a-7)5 + 5²]
= (5a – 2)[(25a² - 70a + 49) – 25a + 35 + 25]
= (5a - 2)[(25a² - 95a + 109)


2.
(a+b)³ + (2a-b)³
= [(a+b) + (2a-b)][(a+b)² -(a+b)(2a-b) + (2a-b)²]
= 3a [(a² + 2ab + b²) - (2a² + ab - b²) + (4a² - 4ab + b²)]
= 3a (3a² - 3ab + b²)

1.-130
2./