Question

How do you multiply `4x(2x^2 + x)`?

Answer 1

`4x(2x^2+x)=8x^3+4x^2`

Explanation:

You would do this by distributing `4x` into the quantities in the parenthesis.

For example,

`a(b+c)=ab+ac`

The `a` was distributed into the parenthesis and multiplied by each unit inside of it. The same concept applies here, we just have expressions instead of constant numbers.

First, distribute the `4x`,

`4x(2x^2+x)=(4x*2x^2)+(4x*x)`

You don't need to add parenthesis, I just added them to clarify how the `4x` was distributed.

Now you can simplify. We can use exponent rules here.

`x^a*x^b=x^(a+b)`

Using this, we can simplify further. Note that the constant coefficients just get multiplied normally.

`4x(2x^2+x)=(4x^1*2x^2)+(4x^1*x^1)=8x^(1+2)+4x^(1+1)=8x^3+4x^2`

Answer 2

`= color(blue)( 8x^3 + 4x^2`

Explanation:

`color(blue)(4x)(2x^2 + x)`
Here `color(blue)(4x)` needs to be multiplied with each term within bracket:

`=color(blue)(4x) . (2x^2 ) + color(blue)(4x).x`
`= color(blue)( 8x^3 + 4x^2`