Question

A student is asked to calculate the value of 353 using the identity (x + y)3 = x3 + 3x2y + 3xy2 + y3. The student's steps are shown below. Step 1: 353 = (30 + 5)3; therefore, x = 30 and y = 5 Step 2: = (x)3 + 3(x)2(y) + 3(x)(y2) + (y)3 Step 3: = (27,000) + (a) + (b) + (125) Step 4: = 42,875 In Step 3, what are the values of a and b, respectively?

Answer 1

(a) = 13,500

(b) = 2,250

Explanation:

Matching Step 3 with Step 2, we see that ...

(a) = 3x^2·y

(b) = 3x·y^2

Filling in the values given for x and y, we have ...

(a) = 3·30^2·5 = 13,500

(b) = 3·30·5^2 = 2,250