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

(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
Simplify terms.
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
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
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