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

120 x^{2} y^{2} + 250 y^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 120 x^{2} y + 250 y^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

120 x^{2} y + 250 y^{3}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 120 x^{2} y - 250 y^{3}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $- 120 x^{2} y - 250 y^{3}$
We know,

$(a - b)^{3} = a^{3} - b^{3} - 3 a b (a - b)$
$(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$

$(2 x - 5 y)^{3} - (2 x + 5 y)^{3}$
$= ((2 x)^{3} - (5 y)^{3} - 3 (2 x) (5 y) (2 x - 5 y)) - ((2 x)^{3} + (5 y)^{3} + 3 (2 x) (5 y) (2 x + 5 y))$
$= (8 x^{3} - 125 y^{3} - 30 x y (2 x - 5 y)) - (8 x^{3} + 125 y^{3} + 30 x y (2 x + 5 y))$

$= 8 x^{3} - 125 y^{3} - 60 x^{2} y + 150 x y^{2} - 8 x^{3} - 125 y^{3} - 60 x^{2} y - 150 x y^{2}$

$= - 250 y^{3} - 120 x^{2} y$
$∴ (2 x - 5 y)^{3} - (2 x + 5 y)^{3} = - 250 y^{3} - 120 x^{2} y$

Suggest Corrections

Similar questions

250 y^{3} - \frac{16}{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} - (2 x + 5 y)^{3}

-

-

Join BYJU'S Learning Program