P((1 + r)^2)^3
To simplify this expression would I distribute first or square the parentheses and tehn cube the numbers in the parenthesis?
P((1+r)^2)^3
combine the exponents
P(1+r)^6
what kind of q is it? you shouldn't be responsible for multiplying that out.
Cd Rollover. Ronnie invested P dollars in a 2-year CD with an annual rate of return of r. After the CD rolled over three times, its value was P((1 + r)^2)^3. Which law of exponents can be used to simplify the expression. Simplify it.
P[(1+r)^6] should be right - and the simplified form; the concept is that each return on the P dollars is calculated by (1+r) increased to another power.
To simplify the expression P((1 + r)^2)^3, you need to follow the order of operations. Start by squaring the expression within the parentheses, and then raise the squared result to the power of 3 (cube it).
Let's go step by step:
Step 1: Square the expression within the parentheses (1 + r)^2.
To do this, you need to multiply (1 + r) by itself. This yields (1 + r)(1 + r) = (1 + r)^2.
Step 2: Cube the result from Step 1.
To cube (1 + r)^2, you need to multiply (1 + r)^2 by itself three times.
So, (1 + r)^2 * (1 + r)^2 * (1 + r)^2.
Step 3: Simplify the expression.
To simplify this further, you can multiply the exponents within each term:
(1 + r)^2 = (1 + r)(1 + r) = 1^2 + 2 * 1 * r + r^2 = 1 + 2r + r^2.
Now, substitute back into the original expression:
(1 + r)^2 * (1 + r)^2 * (1 + r)^2 = (1 + 2r + r^2) * (1 + 2r + r^2) * (1 + 2r + r^2).
To proceed, distribute the terms within each set of parentheses, keeping track of like terms:
(1 + 2r + r^2) * (1 + 2r + r^2) * (1 + 2r + r^2) =
(1*1*1) + (1*1*2r) + (1*1*r^2) + (1*2r*1) + (1*2r*2r) + (1*2r*r^2) + (1*r^2*1) + (1*r^2*2r) + (1*r^2*r^2) +
(2r*1*1) + (2r*1*2r) + (2r*1*r^2) + (2r*2r*1) + (2r*2r*2r) + (2r*2r*r^2) + (2r*r^2*1) + (2r*r^2*2r) + (2r*r^2*r^2) +
(r^2*1*1) + (r^2*1*2r) + (r^2*1*r^2) + (r^2*2r*1) + (r^2*2r*2r) + (r^2*2r*r^2) + (r^2*r^2*1) + (r^2*r^2*2r) + (r^2*r^2*r^2).
Now, simplify each term by multiplying the coefficients and adding the exponents:
1 + 2r + r^2 + 2r + 4r^2 + 2r^3 + r^2 + 2r^3 + r^4 +
2r + 4r^2 + 2r^3 + 4r^2 + 8r^3 + 4r^4 + 2r^3 + 4r^4 + 2r^5 +
r^2 + 2r^3 + r^4 + 2r^3 + 4r^4 + 2r^5 + r^4 + 2r^5 + r^6.
Finally, combine like terms:
1 + 6r + 9r^2 + 18r^3 + 16r^4 + 8r^5 + r^6.
So, the simplified expression is P = 1 + 6r + 9r^2 + 18r^3 + 16r^4 + 8r^5 + r^6.