Adding and subtracting polynomials

The expression to find the perimeter is 12x² - 6, and the perimeter when x= 1.5 is 21

Step-by-step explanation:

The perimeter is the sum of all side lengths for a 2d shape, such as this triangle. Our perimeter is thus

4x² - 3 + 4x² - 2 + 4x² - 1

We can then separate our variables and constants to make it

4x² + 4x² + 4x² - 3 - 2 - 1

Add the constants to get

4x²+4x²+4x²  - 6

To add variables, we must first make sure that they are the same variable/letter as well as to the same degree. The coefficient only affects the result. Because all of our variables are the same letter (x) and are all to the second degree, we can add them. To do this, we simply add the coefficients together to make one big coefficient, and multiply that by the variable. Thus,

4x² + 4x² + 4x² = (4+4+4)x² = 12x²

4x²+4x²+4x²  - 6 = 12x² - 6

Another way of looking at it is that 4x² = 4(x²) = x²+x²+x²+x²

Therefore, the expression to find the perimeter is 12x² - 6, and the perimeter when x= 1.5 is 12 * 1.5² - 6 = 21