How do you find the product $c^2d^3(5cd^7-3c^3d^2-4d^3)$ ?

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Answer 1 · 2016-12-23T16:20:29

$" "5c^3d^10" "-" "3c^5d^5" "-" "4c^2d^6$

$color(blue)("Explaining multiplication rules involving powers ")$

Using a numeric example:

Known that $2xx2=4$

$2xx2" is the same as "2^1xx2^1 =2^(1+1)=2^2=4$

Another example:
$3xx3xx3" is the same as "3^1xx3^1xx3^1 = 3^(1+1+1) = 3^3=27$

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$color(blue)("Answering the question")$

Given: $" "color(blue)(c^2d^3)color(brown)((5cd^7-3c^3d^2-4d^3))$

Multiply everything inside the bracket by $color(blue)(c^2d^3)$

$color(brown)(color(blue)(c^2d^3xx)5cd^7 " "- " "color(blue)(c^2d^3xx)3c^3d^2 " "- " "color(blue)(c^2d^3xx)4d^3)$

$" "5c^3d^10" "-" "3c^5d^5" "-" "4c^2d^6$

How do you find the product c^2d^3(5cd^7-3c^3d^2-4d^3)c^2d^3(5cd^7-3c^3d^2-4d^3)?