# Simplify (5p^2+3p)(p^3-p^2+5) (5p2+3p)(p3-p2+5)
Expand (5p2+3p)(p3-p2+5) by multiplying each term in the first expression by each term in the second expression.
5p2p3+5p2(-p2)+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
Simplify terms.
Simplify each term.
Multiply p2 by p3 by adding the exponents.
Move p3.
5(p3p2)+5p2(-p2)+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
Use the power rule aman=am+n to combine exponents.
5p3+2+5p2(-p2)+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
Add 3 and 2.
5p5+5p2(-p2)+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
5p5+5p2(-p2)+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
Rewrite using the commutative property of multiplication.
5p5+5⋅-1(p2p2)+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
Multiply p2 by p2 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
5p5+5⋅-1p2+2+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
Add 2 and 2.
5p5+5⋅-1p4+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
5p5+5⋅-1p4+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
Multiply 5 by -1.
5p5-5p4+5p2⋅5+3p⋅p3+3p(-p2)+3p⋅5
Multiply 5 by 5.
5p5-5p4+25p2+3p⋅p3+3p(-p2)+3p⋅5
Multiply p by p3 by adding the exponents.
Move p3.
5p5-5p4+25p2+3(p3p)+3p(-p2)+3p⋅5
Multiply p3 by p.
Raise p to the power of 1.
5p5-5p4+25p2+3(p3p1)+3p(-p2)+3p⋅5
Use the power rule aman=am+n to combine exponents.
5p5-5p4+25p2+3p3+1+3p(-p2)+3p⋅5
5p5-5p4+25p2+3p3+1+3p(-p2)+3p⋅5
Add 3 and 1.
5p5-5p4+25p2+3p4+3p(-p2)+3p⋅5
5p5-5p4+25p2+3p4+3p(-p2)+3p⋅5
Rewrite using the commutative property of multiplication.
5p5-5p4+25p2+3p4+3⋅-1(p⋅p2)+3p⋅5
Multiply p by p2 by adding the exponents.
Multiply p by p2.
Raise p to the power of 1.
5p5-5p4+25p2+3p4+3⋅-1(p1p2)+3p⋅5
Use the power rule aman=am+n to combine exponents.
5p5-5p4+25p2+3p4+3⋅-1p1+2+3p⋅5
5p5-5p4+25p2+3p4+3⋅-1p1+2+3p⋅5
Add 1 and 2.
5p5-5p4+25p2+3p4+3⋅-1p3+3p⋅5
5p5-5p4+25p2+3p4+3⋅-1p3+3p⋅5
Multiply 3 by -1.
5p5-5p4+25p2+3p4-3p3+3p⋅5
Multiply 5 by 3.
5p5-5p4+25p2+3p4-3p3+15p
5p5-5p4+25p2+3p4-3p3+15p
Simplify by adding terms.
Add -5p4 and 3p4.
5p5-2p4+25p2-3p3+15p
Move 25p2.
5p5-2p4-3p3+25p2+15p
5p5-2p4-3p3+25p2+15p
5p5-2p4-3p3+25p2+15p
Simplify (5p^2+3p)(p^3-p^2+5)

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