Question

find the value of 125p^3 - 8q^3 if 5p -2q = 1 and pq = 2

Answer 1

The answer is given below :

IDENTITY RULE :

x³ - y³ = (x - y)³ + 3xy(x - y)

SOLUTION :

Now,

125p³ - 8q³

= (5p)³ - (2q)³

= (5p - 2q)³ + 3×5p×2q×(5p - 2q)

= (5p - 2q)³ + 30pq(5p - 2q)

= 1³ + 30×2×1

= 1 + 60

= 61

Thank you for your question.

Answer 2

$125 p^{3}-8 q^{3}=61$

Given:

$125p^{3} - 8q^{3}$

$5p - 2q = 1$

$pq = 2$

To Find:  

Find the value of $125 p^{3}-8 q^{3}$

Answer:

IDENTITY RULE:

$x^{3}-y^{3}=(x-y)^{3}+3 x y(x-y)$

Given that,

$125 p^{3}-8 q^{3}$

$5 p-2 q=1 \ \& \ p q=2$

$=(5 p)^{3}-(2 q)^{3}$

$=(5 p-2 q)^{3}+3 \times 5 p \times 2 q \times(5 p-2 q)$

$=(5 p-2 q)^{3}+30pq (5p-2q)$

$=1^{3}+30 \times 2 \times 1$

$= 1 + 60$

$125 p^{3}-8 q^{3}=61$