分解因式 4(a+b)(a+b)-9(a-b)(a-b)

4(a+b)(a+b)-9(a-b)(a-b)
= [2(a+b)]^2 - [3(a-b)]^2
= [2(a+b)+3(a-b)][2(a+b)-3(a-b)]
= (2a+2b + 3a- 3b) (2a+2b -3a +3b)
= (5a-b) (5b-a)

4(a+b)(a+b)-9(a-b)(a-b)
= [2(a+b)]^2 - [3(a-b)]^2
= [2(a+b)+3(a-b)][2(a+b)-3(a-b)]
= (2a+2b + 3a- 3b) (2a+2b -3a +3b)
= (5a-b) (5b-a)

4(a+b)(a+b)-9(a-b)(a-b)
=2^2(a+b)^2-3^2(a-b)^2
=[2(a+b)]^2-[3(a-b)]^2
=(2a+2b+3a-3b)(2a+2b-3a+3b)
=(5a-b)(5b-a)

A^2-B^2=(A+B)(A-B)

4(a+b)(a+b)-9(a-b)(a-b)
=[4(a+b)^2]-[9(a-b)^2]
=[2^2*(a+b)^2]-[3^2*(a-b)^2]
=[2(a+b)]^2-[3(a-b)]^2
={[2(a+b)]+[3(a-b)]}*{[2(a+b)]-[3(a-b)]}
={2a+2b+[3a-3b]}*{2a+2b-[3a-3b]}
={2a+2b+3a-3b}*{2a+2b-3a+3b}
={5a-b}{-a+5b}
=-5a^2+26b-5b^2

4(a+b)(a+b)-9(a-b)(a-b)
=4(a^2+b^2)-9(a^2+b^2)
=4a^2+4b^2-9a^2-9b^2
=4a^2-9a^2+4b^2-9b^2
=-5a^2-5b^2

2006-10-14 22:59:09 補充：
咦?死, 計錯數, sori 4(a b)(a b)-9(a-b)(a-b) =[4(a b)(a b)]-[9(a-b)(a-b)]=[4(a b)^2]-[9(a-b)^2]=[(a b)^2](4-9)

2006-10-14 23:09:45 補充：
點解出唔到個「加」號既~!?sori 4(a加b)(a加b)-9(a-b)(a-b) =[4(a加b)(a加b)]-[9(a-b)(a-b)]=[4(a加b)^2]-[9(a-b)^2]=[(a加b)^2](4-9)=[4(a加b)^2]-[9(a加b)^2]