Question

a) (6x+1)²+(6x-1)²+2(6x+1)(6x-1)

b)(6x-1)²+(6x+1)²-(12x+2)(6x-1)

c)(ac+bd)²+(ad-bc)²

d)(ac-bd)(ac+bd)

 

Answer 1

a)  Ta có:(6x+1)^2 +(6x-1)^2 +2(6x+1)(6x-1) =[(6x+1)+(6x-1)]^2 =(12x)^2=(12^2)(x^2)=144.x^2

b)  Ta có:(6x+1)^2 +(6x-1)^2 -(12x+2)(6x-1)=(6x+1)^2 +(6x-1)^2 -2(6x+1)(6x-1)=[(6x+1)-(6x-1)]^2=2^2=4

c)  Ta có:(ac+bd)^2 +(ad-bc)^2=(ac)^2 +2(ac)(bd) +(bd^2) +(ad)^2 -2(ad)(bc) +(bc)^2

=a^2.c^2 +2abcd +b^2 d^2 +a^2.d^2 -2abcd +b^2.c^2=a^2.c^2 +b^2.d^2 +a^2.d^2 +b^2.c^2

=(a^2 +b^2)(c^2 +d^2)

d)  Ta có:(ac-bd)(ac+bd)=(ac)^2 -(bd)^2=a^2.c^2 -b^2.d^2