Simplify `(a+b)(c-d)+(a-b)(c-d)+2(ac+bd)

Simplify (a+b+c)(a+b-c)

Let N denote the set of all natural numbers and R be the relation on NxN defined by (a , b)R(c , d), a d(b+c)=b c(a+d)dot Check whether R is an equivalence relation on NXNdot

Let A = N xx N and ** be the binary operation on A defined by (a,b) ** (c,d) = (a + c, b+d) Show that ** is commutative and associative. Find the identity element for ** on A, if any.

If a,b,c and d are four real numbers of the same sign, then the value of (a)/(b)+(b)/(c )+(c )/(d)+(d)/(a) lies in the interval

If a le b le c le d then the equation (x-a)(x-c)+2(x-b)(x-d)=0 has

If a,b,c,d be four distinct positive quantities in GP,then (a) a+dgtb+c (b) c^(-1)d^(-1)+a^(-1)b^(-1)gt2(b^(-1)d^(-1)+a^(-1)c^(-1)-a^(-1)d^(-1))

If sqrt(3)+i=(a+i b)(c+i d) then tan ^(-1) (b/a)+tan ^(-1) (d/c)=

If a,b,c,d be four distinct positive quantities in AP, then (a) bcgtad (b) c^(-1)d^(-1)+a^(-1)b^(-1)gt2(b^(-1)d^(-1)+a^(-1)c^(-1)-a^(-1)d^(-1))

( a+bx) /( a-bx) = ( b+cx)/( b-cx) = ( c +dx)/( c-dx), ( x cancel(=)0) then a,b,c,d are in :

If A={a,b},B={c,d},C={d,e}, then : {(a,c),(a,d),(a,e),(b,c),(b,d),(b,e)} is :