Special product and expansion
If $4 x - 5 z = 2$ and $x z = 6$ , find the value of $64 x^{3} - 125 z^{3}$ .

Open in App

Solution

$64 x^{3} - 125 z^{3} = (4 x)^{3} - (5 z)^{3}$
$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
$= (4 x - 5 z) ((4 x)^{2} + 4 x .5 z + (5 z)^{2})$
Given, $4 x - 5 z = 2$ , $x z = 6$
Squaring
$(4 x)^{2} + 2 \times 4 x .5 z + (5 z)^{2} = 4$
$(4 x)^{2} + (5 z)^{2} = 4 - 40 x z$ ……….. $(1)$
$∴ 64 x^{3} - 125 z^{3} = (4 x - 5 z) (4 - 40 x z + 20 x z)$
$= 2 \times (4 - 20 \times 6)$
$= 2 \times (4 - 120)$
$= 2 \times (- 116)$
$= - 232$ .

Suggest Corrections

Similar questions

Find the value of $64 x^{3} - 125 z^{3}, i f 4 x - 5 z = 16 a n d x z = 12.$

64 x^{2} - 125 z^{3} =

a + b + c = 11

a b + b c + c a = 36

a^{2} + b^{2} + c^{2}

If $4 x - 5 y = 16$ and $x y = 12$ then the value of $64 x^{3} - 125 y^{3} =$ is _______

A. $4648$
B. $15616$
C. $4672$
D. $4696$
E. None of these

f (x) = 64 x^{3} + \frac{1}{x^{3}}

α . β

4 x + \frac{1}{x} = 2

Join BYJU'S Learning Program