Consider the product (x + y + z)2. If the expression is multiplied out and like terms collected, the result is: x2 + y2 + z2 + 2xy + 2yz + 2xz Suppose we do the same to the product (v + w + x + y + z)25 (a) What is the coefficient of the term v9w2x5y7z2? (b) How many different terms are there? (Two terms are the same if the degree of each variable is the same.)

Part a: The coefficient of is

Part b: The number of terms are 23751.

Step-by-step explanation:

part a

From the given equation the

So the coefficient of any term is given as  

Similarly for the generic equation of coefficient of the term in the equation of form is given as  

So now the coefficient of  is given as

The coefficient of is

Part b:

The number of terms is given as

where m is the number of variables which are 5 here

n is the power which is 25 so the number of variables is given as

So the number of terms are 23751.

a) at most means it can cost $12 or less

so the inequality sign would be ≤

you would then need to multiply the number of toppings by the 0.35 for each one and add it to the cost of the cheese pizza.

the equation would be 9.99 + 0.35x ≤ 12

b) using the above equation:

9.99 + 0.35x ≤ 12

subtract 9.99 from each side:

0.35x ≤2.01

divide both sides by 0.35:

x ≤ 2.01 / 0.35

x ≤5.74

at most you could have 5 toppings.

the 5 topping pizza would cost: 0.35 x 5 = 1.75 + 9.99 = $11.74