simplify: (p+q)3 + (p-q)3
Answers
Answer:
(p+q)3+(p-q)3
P3+q3+3pq(p+q)+p3-q3-3pq(p+q)
2p3
Given : (p+q)³ + (p-q)³
To Find : Simplify
Solution:
(p+q)³ + (p-q)³
a³ + b³ = (a + b) ( a² - ab + b²)
a = p + q
b = p - q
= (p + q + p - q) ( (p + q)² - (p + q)(p - q) + ( p - q)²)
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
(a + b)(a - b) = a² - b²
a = p , b = q
= 2p ( p² + 2pq + q² -( p² - q²) + p² - 2pq + q² )
= 2p ( p² + 3q²)
= 2p³ + 6pq²
(p+q)³ + (p-q)³ = 2p³ + 6pq²
Another method:
(p+q)³ + (p-q)³
(a + b)³ = a³ + b³ + 3a²b + 3ab²
(a - b)³ = a³ - b³ - 3a²b + 3ab²
=p³ + q³ + 3p²q + 3pq² + p³ - q³ - 3p²q + 3pq²
= 2p³ + 6pq²
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