Question

分解因式 4(a+b)(a+b)-9(a-b)(a-b)

Answer 1

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
参考: me
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 补充： 咦?死
计错数
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 补充： 点解出唔到个「加」号既~!?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]