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

Mar 11, 2018

$- 3 {x}^{3} + 21 {x}^{2} - 3 x$

Explanation:

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

Multiply
 −3x (x^2−7x+1)

To distribute the $- 3 x ,$ 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 $- 3 x$ to each of the three terms inside the parentheses, like this:

1) -3x xx  x^2 becomes  $- 3 {x}^{3}$

2) $- 3 x \times - 7 x$ becomes  $+ 21 {x}^{2}$

3) $- 3 x \times 1$ becomes  $- 3 x$

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

$- 3 {x}^{3} + 21 {x}^{2} - 3 x$ $\leftarrow$ answer

$\textcolor{w h i t e}{m m m m m m m m}$―――――――

Check

Factoring out any common factors should bring back the original expression

Factor $- 3 x$ from each term

 −3x (x^2−7x+1)   ✓

$C h e c k$