Question 5
Simplify:
$(2 x - 5 y)^{3} - (2 x + 5 y)^{3}$

Open in App

Solution

$(2 x - 5 y)^{3} - (2 x + 5 y)^{3} = [(2 x)^{3} - (5 y)^{3} - 3 (2 x) (5 y) (2 x - 5 y)] - [(2 x)^{3} + (5 y)^{3} + 3 (2 x) (5 y) (2 x + 5 y)]$
$[U s i n g t h e i d e n t i t y, (a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$ and $(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)]$
$= (2 x)^{3} - (5 y)^{3} - 30 x y (2 x - 5 y) - (2 x)^{3} - (5 y) 3 - 30 x y (2 x + 5 y)$
$= - 2 (5 y)^{3} - 30 x y (2 x - 5 y + 2 x + 5 y)$
$= - 2 \times 125 y^{3} - 30 x y (4 x) = - 250 y^{3} - 120 x^{2} y$

Suggest Corrections

Similar questions

Simplify: $(2 x - 5 y)^{3} - (2 x + 5 y)^{3}$ .

(2 x - 5 y)^{3} - (2 x + 5 y)^{3}

{(\frac{x}{2} + \frac{y}{3})}^{3} - {(\frac{x}{2} - \frac{y}{3})}^{3}

{(x + \frac{2}{x})}^{3} + {(x - \frac{2}{x})}^{3}

-

-

(- 2 x + 5 y)^{3}

Join BYJU'S Learning Program

Explore more

Join BYJU'S Learning Program