Question

PLZZ HELP ME!!!!

Write a polynomial that describes the area of the shaded region.

Answer 1

The area of the shaded region is x^2+12x+20

Just took it

Answer 2

The area of the shaded region is
`\boldsymbol{x^2+12x+20} \ \textbf{ square units}`========================================================

Step-by-step explanation:

For now, let's ignore the 4 by 4 smaller square.

The orange larger square has area of...

`(x+6)^2\\\\(x+6)(x+6)\\\\x(x+6)+6(x+6)\\\\x^2+6x+6x+36\\\\x^2+12x+36\\\\`

You can use the FOIL rule to get the same result. The box method is also a visual handy tool.

No matter which method you use, the area of the orange square is
`x^2+12x+36` if we ignore the 4 by 4 portion.

However, we do have that white portion to take away from the orange square. So we'll subtract off 4*4 = 16 square units to end up with
`x^2+12x+36-16 = \boldsymbol{x^2+12x+20}\\\\`

The orange shaded region has area of
`\boldsymbol{x^2+12x+20}`

If we knew what the value of x was, then we could find an actual numeric result rather than a polynomial like this.