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Algebra Level 2

When trumpeting how Singapore topped the PISA test, their newspaper printed

x 2 + 2 x y + y 2 = ( x + y ) ( x − y ) . x^2 + 2xy + y^2 = (x+y) ( x-y).

When is this statement true?

Only when x = − y x=-y or x = 0 x = 0 Only when x = − y x=-y or y = 0 y = 0 Always Only when x = − y x=-y

Chung Kevin by Chung Kevin , 45, Australia

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1 solution

Zach Abueg
Jan 13, 2017

x 2 + 2 x y + y 2 = ( x + y ) ( x + y ) x^2 + 2xy + y^2 = (x + y)(x + y)

( x + y ) ( x + y ) = ( x + y ) ( x − y ) (x + y)(x + y) = (x + y)(x - y)

Because ( x + y ) (x + y) is common to both sides, setting it equal to 0 0 would make both sides equal to 0. 0.

x + y = 0 → x = − y x + y = 0 → x = -y

Once ( x + y ) (x + y) has been canceled, we are left with : :

x + y = x − y x + y = x - y

y = − y y = -y

This is only true when y = 0. y = 0.

The answer is B \boxed{B}

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I think one line has fade up.

Vishwash Kumar ΓΞΩ - 4 years, 4 months ago

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