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(p+7)^3 multiplying a polynomial

User Pojo
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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.

User SomeDude
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