Question

HELP ME!!! What is `π(3x+1)^2` simplified?

Answer 1

`9x^2pi+6xpi+pi`

Explanation:

First, let's expand the question:

`pi*(3x+1)(3x+1)`

Let's multiply `3x+1` by `3x+1` first.

`(3x+1)(3x+1)`

`9x^2+3x+3x+1 rarr` Multiply 3x by 3x and then by 1, multiply 1 by 3x and then by 1

`9x^2+6x+1 rarr` Combine like terms

Now, we have to multiply `9x^2+6x+1` by `pi`.

`9x^2*pi+6x*pi+1*pi rarr` Multiply each term by pi

`9x^2pi+6xpi+pi`

Answer 2

`pi(3x+1)^2=color(blue)(28.27433x^2+18.84956x+3.14159`

Explanation:

Expand:

`pi(3x+1)^2`

Use the formula for the square of a sum:

`(a+b)=a^2+2ab+b^2`,

where:

`a=3x`, `b=1`

`pi((3x)^2+2*3x*1+1^2)`

Simplify.

`pi(9x^2+6x+1)`

Distribute `pi`.

`pi*9x^2+pi*6x+pi*1`

Simplify.

`28.27433x^2+18.84956x+3.14159`

I used the `pi` button on my calculator and rounded off the numbers to five decimal places.

If your calculator does not have a `pi` button, use `3.14159` for `pi`, or ask your teacher what to use for `pi`.