Question

if p-2q=4 value of p3-8q3-24pq-64=?

Answer 1

$Given \:p-2q = 4 \:--(1)$

$\blue { (By \: Algebraic \:Identity )}$

$\boxed { \pink { a^{3} - b^{3} = (a-b)^{3} + 3ab(a-b) }}$

$Here , a = p \: and \: b = 2q$

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

$\implies p^{3} - 8q^{3} = 4^{3} + 6 \times pq\times 4 \: [ From \:(1) ]$

$\implies p^{3} - 8q^{3} = 64 + 24pq$

$\implies p^{3} - 8q^{3} -24pq - 64 = 0$

Therefore.,

$\red { p^{3} - 8q^{3} -24pq - 64 }\green {= 0}$

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