# Factor -p*(2*p^2-3p-1)-(1-2*p+p^2)*(2p^2)

-p⋅(2⋅p2-3p-1)-(1-2⋅p+p2)⋅(2p2)
Factor -p out of -p⋅(2⋅p2-3p-1)-(1-2⋅p+p2)⋅(2p2).
Reorder the expression.
Move 1.
-p⋅(2⋅p2-3p-1)-(-2⋅p+p2+1)⋅(2p2)
Reorder -2⋅p and p2.
-p⋅(2⋅p2-3p-1)-(p2-2⋅p+1)⋅(2p2)
Remove parentheses.
-p⋅(2⋅p2-3p-1)-(p2-2⋅p+1)⋅2p2
Move p2-2⋅p+1.
-p⋅(2⋅p2-3p-1)-1⋅2p2(p2-2⋅p+1)
Reorder -p⋅(2⋅p2-3p-1) and -1⋅2p2(p2-2⋅p+1).
-1⋅2p2(p2-2⋅p+1)-p⋅(2⋅p2-3p-1)
-1⋅2p2(p2-2⋅p+1)-p⋅(2⋅p2-3p-1)
Factor -p out of -1⋅2p2(p2-2⋅p+1).
-p(2p(p2-2⋅p+1))-p(2⋅p2-3p-1)
Factor -p out of -p(2p(p2-2⋅p+1))-p(2⋅p2-3p-1).
-p(2p(p2-2⋅p+1)+2⋅p2-3p-1)
-p(2p(p2-2p+1)+2⋅p2-3p-1)
Apply the distributive property.
-p(2p⋅p2+2p(-2p)+2p⋅1+2⋅p2-3p-1)
Simplify.
Multiply p by p2 by adding the exponents.
Move p2.
-p(2(p2p)+2p(-2p)+2p⋅1+2⋅p2-3p-1)
Multiply p2 by p.
Raise p to the power of 1.
-p(2(p2p1)+2p(-2p)+2p⋅1+2⋅p2-3p-1)
Use the power rule aman=am+n to combine exponents.
-p(2p2+1+2p(-2p)+2p⋅1+2⋅p2-3p-1)
-p(2p2+1+2p(-2p)+2p⋅1+2⋅p2-3p-1)
Add 2 and 1.
-p(2p3+2p(-2p)+2p⋅1+2⋅p2-3p-1)
-p(2p3+2p(-2p)+2p⋅1+2⋅p2-3p-1)
Rewrite using the commutative property of multiplication.
-p(2p3+2⋅-2p⋅p+2p⋅1+2⋅p2-3p-1)
Multiply 2 by 1.
-p(2p3+2⋅-2p⋅p+2p+2⋅p2-3p-1)
-p(2p3+2⋅-2p⋅p+2p+2⋅p2-3p-1)
Simplify each term.
Multiply p by p by adding the exponents.
Move p.
-p(2p3+2⋅-2(p⋅p)+2p+2⋅p2-3p-1)
Multiply p by p.
-p(2p3+2⋅-2p2+2p+2⋅p2-3p-1)
-p(2p3+2⋅-2p2+2p+2⋅p2-3p-1)
Multiply 2 by -2.
-p(2p3-4p2+2p+2⋅p2-3p-1)
-p(2p3-4p2+2p+2⋅p2-3p-1)
Add -4p2 and 2⋅p2.
-p(2p3-2p2+2p-3p-1)
Subtract 3p from 2p.
-p(2p3-2p2-p-1)
Factor -p*(2*p^2-3p-1)-(1-2*p+p^2)*(2p^2)

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