Question

Find the value of 125p^3 - 8p^3, if 5p - 2q = 13 and pq = 30

Answer 1

I think you mistyped 8q^3 as 8p^3

$125 {p}^{3} - 8 {q}^{3}$
could also be written as
${(5p)}^{3} - {(2q)}^{3}$
and this could also be written as
${(5p - 2q)}^{3} + 3pq(p + q)$




We have,
5p - 2q = 13
and
pq = 30

Substitute for them in above expression and you'll get,
${13}^{3} + 3(30)(13) \\ = 2197 + 1170 \\ = 1027$


Hope, you got it.