Question

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

Answer 1

`- 3x^3 +21x^2 - 3x`

Explanation:

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

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Check

Factoring out any common factors should bring back the original expression

Factor `-3x` from each term

`−3x (x^2−7x+1)`   ✓

`Check`