Question

How do you simplify `(−3c−3w^5)^3`?

Answer 1

See a solution process below:

Explanation:

We can use Pascal's Triangle to simplify this expression.

The triangle values for the exponent 3 are:

`color(red)(1)color(white)(.........)color(red)(3)color(white)(.........)color(red)(3)color(white)(.........)color(red)(1)`

We can also write `(-3x - 3w^5)^3` as `(-3x + -3w^5)^3`

Therefore `(color(blue)(-3c) + color(green)(-3w^5))^3` can be multiplied as:

`color(red)(1)(color(green)((-3w^5))^0color(blue)((-3c))^3) + color(red)(3)(color(green)((-3w^5))^1color(blue)((-3c))^2) + color(red)(3)(color(green)((-3w^5))^2color(blue)((-3c))^1) + color(red)(1)(color(green)((-3w^5))^3color(blue)((-3c))^0)`

`(color(red)(1) * color(green)(1) * color(blue)(-27c^3)) + (color(red)(3) * color(green)(-3w^5) * color(blue)(9c^2)) + (color(red)(3) * color(green)(9w^10) * color(blue)(-3c)) + (color(red)(1) * color(green)(-27w^15) * 1)`

`-27c^3 + (-81w^5c^2) + (-81w^10c) + (-27w^15)`

`-27c^3 - 81w^5c^2 - 81w^10c - 27w^15`

`-27c^3 - 81c^2w^5 - 81cw^10 - 27w^15`