Question

How do you multiply `(6a + b)^2`?

Answer 1

`36^2 + 12ab + b^2`

Explanation:

`(6a + b)^2` is the same as saying `(6a + b)(6a + b)`.

We will use the mnemonic `"FOIL"` to solve this equation. `"FOIL"` stand for:
`color(blue)"F"`irsts
`color(purple)"O"`uters
`color(brown)"I"`nners
`color(green)"L"`asts

https://math.tutorvista.com/algebra/foil-method.html

`(6a + b)(6a + b)`

Firsts: `6a xx 6a rarr color(blue)"36a"^color(blue)2`

Outers: `6a xx b rarr color(purple)"6ab"`

Inners: `b xx 6a rarr color(brown)"6ab"`

Lasts: `b xx b rarr color(green)b^color(green)2`

Now put them all together and simplify:

`36^2 + 6ab + 6ab + b^2`

`36^2 + 12ab + b^2`