Question

Multiply.
2x^4 (3x³ − x² + 4x)

Answer 1

Answer: A

Explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer 2

A.
`6x^(7) - 2x^(6) + 8x^(5)`

Step-by-Step

Label the parts of the expression:

Outside the parentheses =
`2x^(4)`

Inside parentheses =
`3x^(3) -x^(2) + 4x`

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

`2x^(4)` ×
`3x^(3)`

`2x^(4)` ×
`-x^(2)`

`2x^(4)` ×
`4x`

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6
`x^(4)x^(3)`

-2
`x^(4)x^(2)`

8
`x^(4) x`

When you multiply exponents together, you multiply the bases as normal and add the exponents together

`6x^(4+3)` =
`6x^(7)`

`-2x^(4+2)` =
`-2x^(6)`

`8x^(4+1)` =
`8x^(5)`

Put the numbers given above into an expression:

`6x^(7) -2x^(6) +8x^(5)`

Key Words

distribution

variable

like exponents