Question

simplify (p+2q)³+(p-2q)³


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Answer 1

Answer:

2p³+24pq²

Step-by-step explanation:

Here, the question is in the form of (a+b) ³. Instead of a we have "p" and instead of b we have "2q" . Now we need to apply the formula a³ + 3a² b + 3ab² + b ³ and we need to apply those values instead of a and b  

(p + 2q)³   = (p)³ + 3 (p)²(2q)+ 3 (p)(2q)² + (2q)³  

              = p³ + 3 (p²)(2q) + 3(p)(4q²) + 8q³

              = p³ + 6p ²q + 12pq² + 8q³

Here, the question is in the form of (a-b) ³. Instead of a we have "p" and instead of b we have "2q" . Now we need to apply the formula a³ + 3a² b + 3ab² + b ³ and we need to apply those values instead of a and b

(p - 2q)³   = (p)³ - 3 (p)²(2q) + 3 (p)(2q)² - (2q)³  

              = p³ - 3 (p²)(2q) + 3(p)(4q²) - 8q³

              = p³ - 6p ²q + 12pq² - 8q³

 Combining both

= (p+2q)³ + (p-2q)³    

= p³ + 6p ²q + 12pq² + 8q³ + p³ - 6p ²q + 12pq² - 8q³

=2p³+24pq²

     

Answer 2

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