How do you find the product #-2d(d^3c^2-4dc^2+2d^2c)+c^2(dc^2-3d^4)#?

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Answer 1 · 2017-07-24T13:54:40

See a solution process below:

First, expand both terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

#color(red)(-2d)(d^3c^2 - 4dc^2 + 2d^2c) + color(blue)(c^2)(dc^2 - 3d^4) =>#

#(color(red)(-2d) * d^3c^2) - (color(red)(-2d) * 4dc^2) + (color(red)(-2d) * 2d^2c) + (color(blue)(c^2) * dc^2) - (color(blue)(c^2) * 3d^4) =>#

#-2d^4c^2 - (-8d^2c^2) + (-4d^3c) + dc^4 - 3d^4c^2 =>#

#-2d^4c^2 + 8d^2c^2 - 4d^3c + dc^4 - 3d^4c^2#

Now, group and combine like terms:

#-2d^4c^2 - 3d^4c^2 + 8d^2c^2 - 4d^3c + dc^4 =>#

#(-2 - 3)d^4c^2 + 8d^2c^2 - 4d^3c + dc^4 =>#

#-5d^4c^2 + 8d^2c^2 - 4d^3c + dc^4 =>#

#-5d^4c^2 - 4d^3c + 8d^2c^2 + dc^4#