Question

If p=2q+6, then what is the value of p3-8q3-36pq-216

Answer 1

Step-by-step explanation:

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Answer 2

The value of $p^3-8q^3-36pq-216$ is 0

Step-by-step explanation:

• Given that p=2q+6
• Given expression is $p^3-8q^3-36pq-216$

To find the value of the given expression :

• First solve the given expression

Substitute the value of p in the given expression we get

• $p^3-8q^3-36pq-216$
• $=(2q+6)^3-8q^3-36q(2q+6)-216$ ( by using the identity $(a+B)^3=a^3+3a^2b+3ab^2+b^3$ and distributive property a(x+y)=ax+ay )
• $=(2q)^3+3(2q)^2(6)+3(2q)(6)^2+6^3-8q^3-36q(2q)-36q(6)-216$
• $=(2)^3(q)^3+18(2)^2(q)^2+6q(36)+216-8q^3-72q^{1+1}-216q-216$

( by using the identity $a^m.a^n=a^{m+n}$ )

• $=8q^3+72q^2+216q-8q^3-72q^2-216q$ ( adding the like terms )
• $=0$

Therefore $p^3-8q^3-36pq-216=0$

Therefore the value of $p^3-8q^3-36pq-216$ is 0