Homework Help

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

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galbenusa | Student, Grade 10 | eNoter

Posted June 7, 2011 at 1:50 AM via web

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Evaluate the product

 (x+x/y)*(x-x/y) for x=30 and y=15.

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3 Answers | Add Yours

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giorgiana1976 | College Teacher | Valedictorian

Posted June 7, 2011 at 4:50 AM (Answer #2)

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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

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academicsfirst | High School Teacher | (Level 2) Adjunct Educator

Posted June 12, 2011 at 10:45 AM (Answer #3)

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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.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 2, 2012 at 5:29 AM (Answer #4)

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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

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