# Simplify -3xy^2z(2xy+5x^2z-4yz^3)

-3xy2z(2xy+5x2z-4yz3)
Apply the distributive property.
-3xy2z(2xy)-3xy2z(5x2z)-3xy2z(-4yz3)
Simplify.
Multiply x by x by adding the exponents.
Move x.
-3(x⋅x)y2z(2y)-3xy2z(5x2z)-3xy2z(-4yz3)
Multiply x by x.
-3x2y2z(2y)-3xy2z(5x2z)-3xy2z(-4yz3)
-3x2y2z(2y)-3xy2z(5x2z)-3xy2z(-4yz3)
Multiply x by x2 by adding the exponents.
Move x2.
-3x2y2z(2y)-3(x2x)y2z(5z)-3xy2z(-4yz3)
Multiply x2 by x.
Raise x to the power of 1.
-3x2y2z(2y)-3(x2x1)y2z(5z)-3xy2z(-4yz3)
Use the power rule aman=am+n to combine exponents.
-3x2y2z(2y)-3×2+1y2z(5z)-3xy2z(-4yz3)
-3x2y2z(2y)-3×2+1y2z(5z)-3xy2z(-4yz3)
-3x2y2z(2y)-3x3y2z(5z)-3xy2z(-4yz3)
-3x2y2z(2y)-3x3y2z(5z)-3xy2z(-4yz3)
Multiply y2 by y by adding the exponents.
Move y.
-3x2y2z(2y)-3x3y2z(5z)-3x(y⋅y2)z(-4z3)
Multiply y by y2.
Raise y to the power of 1.
-3x2y2z(2y)-3x3y2z(5z)-3x(y1y2)z(-4z3)
Use the power rule aman=am+n to combine exponents.
-3x2y2z(2y)-3x3y2z(5z)-3xy1+2z(-4z3)
-3x2y2z(2y)-3x3y2z(5z)-3xy1+2z(-4z3)
-3x2y2z(2y)-3x3y2z(5z)-3xy3z(-4z3)
-3x2y2z(2y)-3x3y2z(5z)-3xy3z(-4z3)
-3x2y2z(2y)-3x3y2z(5z)-3xy3z(-4z3)
Simplify each term.
Multiply y2 by y by adding the exponents.
Move y.
-3×2(y⋅y2)z⋅2-3x3y2z(5z)-3xy3z(-4z3)
Multiply y by y2.
Raise y to the power of 1.
-3×2(y1y2)z⋅2-3x3y2z(5z)-3xy3z(-4z3)
Use the power rule aman=am+n to combine exponents.
-3x2y1+2z⋅2-3x3y2z(5z)-3xy3z(-4z3)
-3x2y1+2z⋅2-3x3y2z(5z)-3xy3z(-4z3)
-3x2y3z⋅2-3x3y2z(5z)-3xy3z(-4z3)
-3x2y3z⋅2-3x3y2z(5z)-3xy3z(-4z3)
Multiply 2 by -3.
-6x2y3z-3x3y2z(5z)-3xy3z(-4z3)
Multiply z by z by adding the exponents.
Move z.
-6x2y3z-3x3y2(z⋅z)⋅5-3xy3z(-4z3)
Multiply z by z.
-6x2y3z-3x3y2z2⋅5-3xy3z(-4z3)
-6x2y3z-3x3y2z2⋅5-3xy3z(-4z3)
Multiply 5 by -3.
-6x2y3z-15x3y2z2-3xy3z(-4z3)
Multiply z by z3 by adding the exponents.
Move z3.
-6x2y3z-15x3y2z2-3xy3(z3z)⋅-4
Multiply z3 by z.
Raise z to the power of 1.
-6x2y3z-15x3y2z2-3xy3(z3z1)⋅-4
Use the power rule aman=am+n to combine exponents.
-6x2y3z-15x3y2z2-3xy3z3+1⋅-4
-6x2y3z-15x3y2z2-3xy3z3+1⋅-4