Question

How do you multiply `(4x + 5)^2`?

Answer 1

`16x^2+40x+25`

Explanation:

`(4x+5)^2=(4x+5)(4x+5)`

`"each term in the second factor is multiplied by "`
`"each term in the first factor"`

`rArr(color(red)(4x+5))(4x+5)`

`=color(red)(4x)(4x+5)color(red)(+5)(4x+5)`

`"distribute each product"`

`=16x^2+20x+20x+25`

`=16x^2+40x+25larrcolor(blue)"collect like terms"`

Answer 2

`16x^2+40x+25`

Explanation:

Use the FOIL method, or the shortcut for squaring binomials.

For any `x` and `y`, `(x+y)^2=x^2+2xy+y^2`

Our `x` is `4x` and our `y` is `5`.

Therefore:

`(4x+5)^2=(4x)^2+2(4x*5)+(5)^2`

`(4x+5)^2=16x^2+40x+25`

Alternatively, you could multiply 'each by each,' using the FOIL method.

Answer 3

See a solution process below:

Explanation:

We can use this rule for quadratics:

`(color(red)(x) + color(blue)(y))^2 = (color(red)(x) + color(blue)(y))(color(red)(x) + color(blue)(y)) = color(red)(x)^2 + 2color(red)(x)color(blue)(y) + color(blue)(y)^2`

Let:

`color(red)(x) = 4x`

`color(blue)(y) = 5`

Substituting gives:

`(color(red)(4x) + color(blue)(5))^2 =>`

`(color(red)(4x) + color(blue)(5))(color(red)(4x) + color(blue)(5)) =>`

`16x^2 + 40x + 25`

Answer 4

`=16x^2 + 40x + 25`

Explanation:

`(4x + 5)^2`

As you can see, each users are solving it differently and this is what makes Math funny and unique. There are different steps, strategies you can use to solve a problem.

Well, I'm gonna use my favorite method which is Distributive

So let's start:

`=(4x)(4x)+(4x)(5)+(5)(4x)+(5)(5)`

`=16x^2 + 20x + 20x + 25`

`=16x^2 + 40x + 25`