Question

Simplify (x/3+y/5)^3 - (x/3-y/5)^3

Answer 1

Solution:::::::------

=》[X/3 + Y/5]^3 - [X/3 - Y/5]^3
=》[X/3+Y/5+X/3-Y/3]^3 -3[X/3+Y/5][X/3-Y/5][X/3+Y/5+X/3+Y/5]
=》[2x/3]^3 - 3[X^2/9-Y^2/25][2x/3]
=》8x^3/27 - [x^2/3 - 2y^2/25]2x/3
=》8x^3/27-2x^3/9+6xy^2/75

=》6xy^2/75 ANS...

Answer 2

Answer:

$(\frac{x}{3}+\frac{y}{5})^3-(\frac{x}{3}-\frac{y}{5})^3=\frac{2y^3}{125}+\frac{2x^y}{15}$

Step-by-step explanation:

Given : Expression $(\frac{x}{3}+\frac{y}{5})^3-(\frac{x}{3}-\frac{y}{5})^3$

To find : Simplify the expression ?

Solution :

Using cubic identity,

$(a+b)^3=a^3+b^3+3ab(a+b)$

$(a-b)^3=a^3-b^3-3ab(a-b)$

$(\frac{x}{3}+\frac{y}{5})^3-(\frac{x}{3}-\frac{y}{5})^3$

$=(\frac{x}{3})^3+(\frac{y}{5})^3+3\times\frac{x}{3}\times\frac{y}{5}(\frac{x}{3}+\frac{y}{5})-((\frac{x}{3})^3-(\frac{y}{5})^3-3\times\frac{x}{3}\times\frac{y}{5}(\frac{x}{3}-\frac{y}{5}))$

$=(\frac{x}{3})^3+(\frac{y}{5})^3+\frac{xy}{5}(\frac{5x+3y}{15})-(\frac{x}{3})^3+(\frac{y}{5})^3+\frac{xy}{5}(\frac{5x-3y}{15})$

$=2(\frac{y}{5})^3+\frac{xy}{5}(\frac{5x+3y}{15}+\frac{5x-3y}{15})$

$=2(\frac{y^3}{125})+\frac{xy}{5}(\frac{5x+3y+5x-3y}{15})$

$=\frac{2y^3}{125}+\frac{xy}{5}(\frac{10x}{15})$

$=\frac{2y^3}{125}+\frac{2x^y}{15}$

Therefore, $(\frac{x}{3}+\frac{y}{5})^3-(\frac{x}{3}-\frac{y}{5})^3=\frac{2y^3}{125}+\frac{2x^y}{15}$