Multiply -y(4z^3-3z^2y+zy^2+5y^3)

Math
-y(4z3-3z2y+zy2+5y3)
Apply the distributive property.
-y(4z3)-y(-3z2y)-y(zy2)-y(5y3)
Simplify.
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Rewrite using the commutative property of multiplication.
-1⋅4(yz3)-y(-3z2y)-y(zy2)-y(5y3)
Multiply y by y by adding the exponents.
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Move y.
-1⋅4(yz3)-(y⋅y)(-3z2)-y(zy2)-y(5y3)
Multiply y by y.
-1⋅4(yz3)-y2(-3z2)-y(zy2)-y(5y3)
-1⋅4(yz3)-y2(-3z2)-y(zy2)-y(5y3)
Multiply y by y2 by adding the exponents.
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Move y2.
-1⋅4(yz3)-y2(-3z2)-(y2y)z-y(5y3)
Multiply y2 by y.
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Raise y to the power of 1.
-1⋅4(yz3)-y2(-3z2)-(y2y1)z-y(5y3)
Use the power rule aman=am+n to combine exponents.
-1⋅4(yz3)-y2(-3z2)-y2+1z-y(5y3)
-1⋅4(yz3)-y2(-3z2)-y2+1z-y(5y3)
Add 2 and 1.
-1⋅4(yz3)-y2(-3z2)-y3z-y(5y3)
-1⋅4(yz3)-y2(-3z2)-y3z-y(5y3)
Rewrite using the commutative property of multiplication.
-1⋅4(yz3)-y2(-3z2)-y3z-1⋅5(y⋅y3)
-1⋅4(yz3)-y2(-3z2)-y3z-1⋅5(y⋅y3)
Simplify each term.
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Multiply -1 by 4.
-4(yz3)-y2(-3z2)-y3z-1⋅5(y⋅y3)
Rewrite using the commutative property of multiplication.
-4yz3-1⋅-3(y2z2)-y3z-1⋅5(y⋅y3)
Multiply -1 by -3.
-4yz3+3(y2z2)-y3z-1⋅5(y⋅y3)
Multiply y by y3 by adding the exponents.
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Multiply y by y3.
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Raise y to the power of 1.
-4yz3+3y2z2-y3z-1⋅5(y1y3)
Use the power rule aman=am+n to combine exponents.
-4yz3+3y2z2-y3z-1⋅5y1+3
-4yz3+3y2z2-y3z-1⋅5y1+3
Add 1 and 3.
-4yz3+3y2z2-y3z-1⋅5y4
-4yz3+3y2z2-y3z-1⋅5y4
Multiply -1 by 5.
-4yz3+3y2z2-y3z-5y4
-4yz3+3y2z2-y3z-5y4
Multiply -y(4z^3-3z^2y+zy^2+5y^3)

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