(2p-1)(4p2+2p+1)

Expand (2p-1)(4p2+2p+1) by multiplying each term in the first expression by each term in the second expression.

2p(4p2)+2p(2p)+2p⋅1-1(4p2)-1(2p)-1⋅1

Combine the opposite terms in 2p(4p2)+2p(2p)+2p⋅1-1(4p2)-1(2p)-1⋅1.

Reorder the factors in the terms 2p⋅1 and -1(2p).

2p(4p2)+2p(2p)+1⋅2p-1(4p2)-1⋅2p-1⋅1

Subtract 2p from 1⋅2p.

2p(4p2)+2p(2p)-1(4p2)+0-1⋅1

Add 2p(4p2)+2p(2p)-1(4p2) and 0.

2p(4p2)+2p(2p)-1(4p2)-1⋅1

2p(4p2)+2p(2p)-1(4p2)-1⋅1

Simplify each term.

Rewrite using the commutative property of multiplication.

2⋅4(p⋅p2)+2p(2p)-1(4p2)-1⋅1

Multiply p by p2 by adding the exponents.

Multiply p by p2.

Raise p to the power of 1.

2⋅4(p1p2)+2p(2p)-1(4p2)-1⋅1

Use the power rule aman=am+n to combine exponents.

2⋅4p1+2+2p(2p)-1(4p2)-1⋅1

2⋅4p1+2+2p(2p)-1(4p2)-1⋅1

Add 1 and 2.

2⋅4p3+2p(2p)-1(4p2)-1⋅1

2⋅4p3+2p(2p)-1(4p2)-1⋅1

Multiply 2 by 4.

8p3+2p(2p)-1(4p2)-1⋅1

Multiply p by p.

8p3+2⋅2p2-1(4p2)-1⋅1

Multiply 2 by 2.

8p3+4p2-1(4p2)-1⋅1

Multiply 4 by -1.

8p3+4p2-4p2-1⋅1

Multiply -1 by 1.

8p3+4p2-4p2-1

8p3+4p2-4p2-1

Combine the opposite terms in 8p3+4p2-4p2-1.

Subtract 4p2 from 4p2.

8p3+0-1

Add 8p3 and 0.

8p3-1

8p3-1

8p3-1

Multiply (2p-1)(4p^2+2p+1)