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(482^2+2(482)(118)+118^2)/ 306^2−294^2=
[#permalink]
11 Apr 2020, 11:20
11 Apr 2020, 11:20
Expert Reply
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Question Stats:
88% (01:41) correct
11% (03:01) wrong based on 9 sessions
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Joined: 10 Apr 2015
Posts: 6218
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Re: (482^2+2(482)(118)+118^2)/ 306^2−294^2=
[#permalink]
11 Apr 2020, 11:20
11 Apr 2020, 11:20
3 special factorizations:
#1: \(x^2 + 2xy +y^2 = (x + y)(x + y) = (x + y)^2\)
#2: \(x^2 - 2xy +y^2 = (x - y)(x - y) = (x - y)^2\)
#3: \(x^2 -y^2 = (x + y)(x - y)\)
Take: \(\frac{482^2+2(482)(118)+118^2}{ 306^2−294^2}\)
Apply factorization #1 to the numerator, and factorization #3 to the denominator to get: \(\frac{(482+118)(482+118)}{ (306+294)(306-294)}\)
Evaluate the parts in brackets: \(\frac{(600)(600)}{ (600)(12)}\)
Simplify: \(\frac{600}{ 12}\)
Evaluate: 50
Cheers,
Brent
#1: \(x^2 + 2xy +y^2 = (x + y)(x + y) = (x + y)^2\)
#2: \(x^2 - 2xy +y^2 = (x - y)(x - y) = (x - y)^2\)
#3: \(x^2 -y^2 = (x + y)(x - y)\)
Take: \(\frac{482^2+2(482)(118)+118^2}{ 306^2−294^2}\)
Apply factorization #1 to the numerator, and factorization #3 to the denominator to get: \(\frac{(482+118)(482+118)}{ (306+294)(306-294)}\)
Evaluate the parts in brackets: \(\frac{(600)(600)}{ (600)(12)}\)
Simplify: \(\frac{600}{ 12}\)
Evaluate: 50
Cheers,
Brent
gmatclubot
Re: (482^2+2(482)(118)+118^2)/ 306^2−294^2= [#permalink]
11 Apr 2020, 11:20
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