" 6."(x+y)/(2)-(x-y)/(3)=8,(x+y)/(3)+(x-y)/(4)=4

Simplify : (x+y)^(4) - 4y(x+y)^(3) + 6y^(2)(x+y)^(2)-4y^(3)(x+y)+y^(4)

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

3-8 (2x-y) +4 (2x-y) ^ (2)

(x-4)(x-3)=(x-6)(x-5) (y-9)(y-3)= (y-4)(y-3)

The following are the steps involved in factorizing 64 x^(6) -y^(6) . Arrange them in sequential order (A) {(2x)^(3) + y^(3)} {(2x)^(3) - y^(3)} (B) (8x^(3))^(2) - (y^(3))^(2) (C) (8x^(3) + y^(3)) (8x^(3) -y^(3)) (D) (2x + y) (4x^(2) -2xy + y^(2)) (2x - y) (4x^(2) + 2xy + y^(2))

If (3x -4y) : (2x -3y) = (5x -6y) : (4x -5y) , find : x : y .

Find the LCM of 6x ^(2) y ^(3), 8x ^(3) y ^(2) , 12 x ^(4) y ^(3) and 10 x ^(3) y ^(4).

Factorize each of the following algebraic expressions: (1) (x-y)^2+(x-y) (2) 6(a+2b)-4(a+2b)^2 (3) a(x-y)+2b(y-x)+c(x-y)^2 (4) -4\ (x-2y)^2+8(x-2y)