How do you multiply #-3x(x^2-7x+1)#?

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Answer 1 · 2018-03-11T10:27:56

#- 3x^3 +21x^2 - 3x#

This is a Distributive Law question about the multiplication of exponents.

Multiply
# −3x (x^2−7x+1)#

To distribute the #-3x,# you multiply it with each of the three terms inside the parentheses.

To multiply the exponents of like bases, you add.

So one at a time, you distribute #-3x# to each of the three terms inside the parentheses, like this:

1) #-3x xx x^2# becomes #-3x^3#

2) #-3x xx - 7x# becomes #+21 x^2#

3) #-3x xx 1# becomes #-3x#

When you write the three answers in a line, you get this:

#- 3x^3 +21x^2 - 3x# #larr# answer

#color(white)(mmmmmmmm)#―――――――

Check

Factoring out any common factors should bring back the original expression

Factor #-3x# from each term

# −3x (x^2−7x+1)# ✓

#Check#