MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Distributive Property of Multiplication

Find the valu...

Question

Find the value of $8 x^{3} - y^{3},$ if $2 x - y = 12$ and $x y = 4$ .

A

2016

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

B

2017

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

C

2018

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

D

2019

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

Open in App

Solution

The correct option is A $2016$
$2 x - y = 12$ and $x y = 4$

$8 x^{3} - y^{3} = (2 x)^{3} - y^{3}$
$= (2 x - y) ((2 x)^{2} + y^{2} + 2 x y)$ [Using $a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$ ]

$= (2 x - y) [(2 x - y)^{2} + 2 \times 2 x \times y + 2 x y]$
[Using $a^{2} + b^{2} = (a - b)^{2} + 2 a b$ ]

$= (2 x - y) [(2 x - y)^{2} + 6 x y]$

On substituting the values, $2 x - y = 12$ and $x y = 4$ , we get,
$= 12 \times [(12)^{2} + 6 (4)]$
$= 12 [144 + 24]$
$= 12 \times 168 = 2016$

Suggest Corrections

thumbs-up

0

Similar questions

Q. IF 2x+y=3 , xy=1 , then the value of

8 x^{3} + y^{3}

2 x + 3 y = 13

x y = 6

, find the value of

8 x^{3} + 21 y^{3}

.

2 x + 3 y = 12

x y = 6

, find the value of

8 x^{3} + 27 y^{3}

2 x + \frac{y}{3} = 12 and x y = 30, then 8 x^{3} + \frac{y^{3}}{27} =_______

(a) 1008
(b) 168
(c) 106
(d) none of these

x + y = 12

x y = 27

, find the value of

x^{3} + y^{3}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Distributivity for Algebraic Expressions

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Distributive Property of Multiplication

Standard VIII Mathematics

Join BYJU'S Learning Program

CrossIcon