中3數學題,求解答2題

Factorize?

2012-07-22 16:12:02 補充：
I assume you want to factorize them. 1) (2a + b)(2a - b) - 4a + 1= 4a² - b² - 4a + 1= (2a - 1)² - b²= (2a - b - 1)(2a + b - 1)2) a³ + b³ - a²b - ab²= a²(a -b) - b²(a -b)= (a - b)(a² - b²)= (a - b)(a - b)(a + b)= (a - b)²(a + b) P.S.Important identities:i) x² - y² = (x - y)(x + y)ii) x² ± 2xy + y² = (x ± y)² HOPE THIS CAN HELP YOU! ~ ^_^

1.(2a+b)(2a-b)-4a+1
=(2a+b)(2a)-(2a+b)(b)-4a+1
=4a^2+2ab-2ab-b^2-4a+1
=4a^2-b^2-4a+1

2.a^3+b^3-a^2b-ab^2
=a^3+b^3-ab(a+b)
=(a+b)^3-ab(a+b)
=(a+b)(a-ab+b)

2012-07-22 16:29:41 補充：
PS: 第2題更正!!

2.a^3+b^3-a^2b-ab^2
=a^2(a-b)+b^2(b-a)
=a^2(a-b)-b^2(a-b)
=(a^2-b^2)(a-b)
=(a-b)(a^2-b^2)
=(a-b)(a-b)(a+b)
=(a-b)^2(a+b)