# Evaluate the product  (x+x/y)*(x-x/y) for x=30 and y=15.

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

Notice that the product (x+x/y)(x-x/y) consists of the terms x and x/y, hence, you need to substitute 30 for x and 15 for y such that:

(30 + 30/15)(30 - 30/15) = (30+2)(30-2)

(30 + 30/15)(30 - 30/15) = 32*28

(30 + 30/15)(30 - 30/15) = 896

Posted on

We are asked to find the product of (x + x/y) * (x -x/y) when x = 30 and y =15.

We will substitute the given values of x  = 30 and y = 15 into the expression.

=> ( x + x/y) * (x - x/y)

=> ( 30 + 30/15) * ( 30 - 30/15)

=> ( 30 + 2) * ( 30 - 2)

=> (32) * (28)

=> 896

The product is 896.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We notice that the product could be transformed into a difference of squares:

(x+x/y)*(x-x/y) = x^2 - (x/y)^2

x^2 - (x/y)^2 = x^2 - x^2/y^2

We'll factorize by x^2:

x^2 - x^2/y^2 = x^2*(1 - 1/y^2)

Now, we'll substitute x and y into the given expression:

x^2*(1 - 1/y^2) = 900*(1 - 1/225)

We'll re-write the expression:

900*(1 - 1/225) = 900(225-1)/225

900*(1 - 1/225) = 900*224/225

900*(1 - 1/225) = 4*224

900*(1 - 1/225) = 896

We also could write the difference of squares, 25 - 1, as:

225 - 1 = (15-1)(15+1) = 14*16

(x+x/y)*(x-x/y) = 896