P dollars is invested at annual interest rate for 1 year. if the interest is compounded semiannually, then the polynomial p(1+r/2)^2 represents the value of the investment after 1 year. could you rewrite this expression without parentheses. Evaluate the polynomial if p = $200 and r = 10

(1+r/2)^2 = 1 + r + 1/4 *r^2

Put in the value of p, and r, and evaluate. I will be happy to critique your work or thinking.

Check my work.

Explain Bot Explain Bot answered

To rewrite the expression without parentheses, we can expand the binomial using the formula (a+b)^2 = a^2 + 2ab + b^2.

Starting with the expression (1+r/2)^2, we can rewrite it as:
(1+r/2)(1+r/2)
Using the formula for multiplying binomials, we obtain:
1 + r/2 + r/2 + (r/2)^2
Simplifying the terms, we have:
1 + r + r/2 + r^2/4
Now, we can simplify the expression further:
1 + r + 1/2r + (1/4)r^2
Combining like terms, we get the final expression without parentheses:
1 + (3/2)r + (1/4)r^2

Now, let's evaluate the polynomial if p = $200 and r = 10:
Value = p(1+r/2)^2
Substituting in the given values, we have:
Value = $200(1+10/2)^2
Value = $200(1+5)^2
Value = $200(6)^2
Value = $200(36)
Value = $7200

Therefore, if p = $200 and r = 10, the value of the investment after 1 year is $7200.