The expanded form of the cube of the binomial ( p + 7 )³ is p³ + 21p² + 147p + 343.
Given the cube of the binomial in the question:
( p + 7 )³
To expand the cube of the binomial ( p + 7 )³, we can use the binomial expansion formula or simply multiply the binomial by itself three times.
Here, we expand by multiplying:
( p + 7 )³ = ( p + 7 )( p + 7 )( p + 7 )
( p + 7 )³ = ( p + 7 )[( p + 7 )( p + 7 )]
( p + 7 )³ = ( p + 7 )[ p( p + 7 ) + 7( p + 7) ]
( p + 7 )³ = ( p + 7 )[ p² + 7p + 7p + 49 ]
( p + 7 )³ = ( p + 7 )[ p² + 14p + 49 ]
( p + 7 )³ = p( p² + 14p + 49 ) + 7( p² + 14p + 49 )
( p + 7 )³ = p³ + 14p² + 49p + 7p² + 98p + 343
Collect and add like terms:
( p + 7 )³ = p³ + 14p² + 7p² + 98p + 49p + 343
( p + 7 )³ = p³ + 21p² + 147p + 343
Therefore, the expanded form is p³ + 21p² + 147p + 343.
This question is not complete, the complete question is:
Expand the polynomial ( p + 7 )³ by multiplying a polynomial.