1/4(a-b)^2+3(a-b)(a+b)+9(a+b)^2

1/4(a-b)^2+3(a-b)(a+b)+9(a+b)^2
1/4(a-b)^2+3(a-b)(a+b)+9(a+b)^2

1/4(a-b)^2+3(a-b)(a+b)+9(a+b)^2
1/4(a-b)^2+3(a-b)(a+b)+9(a+b)^2
=[1/2(a-b)+3(a+b)]^2
=[a/2-b/2+3a+3b]^2
=[7a/2+5b/2)^2

设x=a-b, y=a+b
那么原式＝1/4*x^2+3x*y+9*y^2=(1/2*x+3y)^2=(1/2*a-1/2*b+3a+3b)^2=(3.5a+2.5b)^2