How do you multiply #6x^2(-2x^2+5x-30)#?

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Answer 1 · 2017-07-03T15:59:24

See a solution process below:

Multiply each term within the parenthesis by the term outside the parenthesis:

#color(red)(6x^2)(-2x^2 + 5x - 30) =>#

#(color(red)(6x^2) xx -2x^2) + (color(red)(6x^2) xx 5x) - (color(red)(6x^2) xx 30)#

Use this rule of exponents to multiply the variables in the individual terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#-12x^4 + 30x^3 - 180x^2#

Answer 2 · 2017-07-03T16:00:27

You distribute the #6x^2# throughout the polynomial.

#6x^2 * (-2x^2) = -12x^4#

#6x^2 * 5x = 30x^3#

#6x^2 * (-30) = -180x^2#

So, your answer is

#-12x^4 + 30x^3 - 180x^2#