Can these expressions be simplified (i.e., reduced to a single term) ?
A. `x^(2)+x^(2)`
B.` x^(2)*y^(2)`
C. `(2^(n)+3^(n))`

Simplify by reducing to a single term : sin (x -y) cos x - cos (x-y) sin x.

Simplify these expressions and find their values if x=3, a-1 and b=-2 (i) 3x-5-x+9

If A be the sum of odd terms and B be the sum of even terms in the expansion of (x+a)^(n) , prove that A^(2) -B^(2) = (x^(2) - a^(2)) ^(n)

Find the sum of n terms of the series (x+y)+(x^(2)+2y)+(x^(3)+3y)+...

Simplify the expressions and evaluate them as directed: (i) x(x-3)+2 for x=1 (ii) 3y(2y-7)-3(y-4)-63 for y=2

Simplify the expression 8(x^(2)-x-1) + 5 (2x-2) - 3 (x^(2) +x - 1)

Simplify and find the value of the simplified expression when x=-1 and y=2. 3(2x^2-4y^2)- [7xy-[3(x^3-2y^2)-2xy)]

If o be the sum of odd terms and E that of even terms in the expansion of (x+a)^n prove that: (i) O^2-E^2=(x^2-a^2)^n (ii) 4O E=(x+a)^(2n)-(x-a)^(2n) (iii) 2(O^2+E^2)=(x+a)^(2n)+(x-a)^(2n)

Simplify and find the value of the simplified expression when x=-1 and y=2. 4(x^2+3y^2)-(9xy-[5(2x^3-3y^2)+xy)]