Question

Find each square (x+4)^2

Answer 1

Explanation:

(x+4)^2

you can also expand it

(x+4)(x+4)

x^2+4x+4x+16

x^2+8x+16

Answer 2

`x^(2) +8x+16`

Explanation:

There are 2 ways to find the square of a binomial. You can use FOIL or use a formula. Just remember that the square of a binomial will always be a trinomial.

FOIL

Since we are squaring a binomial we can rewrite the expression as (x+4) * (x+4). FOIL stands for First, Outside, Inside, Last. This explains how to multiply out 2 binomials. This method will give you 4 different terms that can then be combined to find the answer.

First - multiply the first terms of each binomial

• x * x =
  `x^(2)`

Outside - multiply the terms on the outside of both binomials

• x * 4 = 4x

Inside - multiply the terms on the inside of both binomials

• 4 * x = 4x

Last - multiply the last terms of each binomial

• 4 * 4 = 16

Now we can combine these terms to create the new polynomial
`x^(2) +4x+4x+16`. Then, combine like terms for the final answer:
`x^(2) +8x+16`.

Shortcut

Another way to square binomials is to use the formula
`a^(2) +2ab+b^(2)`, where a is the first term and b is the second term. So, for this formula, the binomial would look like (a+b).

So, we can apply this formula by plugging in x for a and 4 for b.

• 
  `x^2+2*4*x+4^2`

Then, multiply the middle term

• 
  `x^(2) +8x+4^2`

Finally, square 4

• 
  `x^2+8x+16`

This gives us the same final answer as the method above.