Respuesta :

luisejr77

Answer: [tex]x^2+8x+16[/tex]

Step-by-step explanation:

It is important to remember that the formula for calculate the area of a square is:

[tex]A=s^2[/tex]

Where "s" is the side lenght of the square.

From the figure you can identify that the side lenght of the square can be represented with this expression:

[tex]x+4[/tex]

Therefore, the following expression represents the area of the square:

[tex](x+4)^2[/tex]

In order to simplify it, you need to remember that:

[tex](a\±b)^2=a^2\±2ab+b^2[/tex]

Then, you get that the polynomial that represents the area of the given square, is:

[tex]=x^2+2(x)(4)+4^2=x^2+8x+16[/tex]

rahulsharma789888

The polynomial that represents the area of the square

[tex]\rm \bold{ x^2 +8x +16}[/tex]

Let the side of square be "b"

so the area of square is written as

[tex]\rm A = b^2 \\Where\; A = Area \\and \; b = length\; of \; the \; side \\[/tex]  

So according to the given figure

Length of one side in the given equation = 4+ x

[tex]\rm Area\; of \; square\; can \; be \; represented\; as \\(4+x) \times (4+x)[/tex]

According to the identity

[tex]\rm (a +b)^2 = a^2 +b^2 +2ab ........(1)[/tex]

On solving further according to the identity formulated in equation (1)  we get

[tex]\rm Area \; of\; the \; new \; sqaure = (4+x)^2 = 16 +x^2 + 2\times 4\times x \\(4+x)^2 = x^2 +8x +16[/tex]

So, The polynomial that represents the area of the square

[tex]\rm \bold{ x^2 +8x +16}[/tex]

For more information please refer to the link below

https://brainly.com/question/1658516

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