Catching some Zs

Algebra Level 1

After multiplication and being written as a polynomial, ( a + b ) ( x + y + z ) (a+b)(x+y+z) includes the term 2 z 2 . 2z^2 . Also, x , x, y , y, and z z are distinct. Assuming one of the multiple choice options given is true, which one is true?

a = b = z a = b = z a = b 2 = z a = b^2 = z a = b = z a = b = \sqrt{z} a = z − b a = z - b

Jason Dyer by Jason Dyer

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1 solution

Jason Dyer Staff
Oct 11, 2016

Considering just the z z portion of the multiplication, ( a + b ) ( z ) = a z + b z (a + b)(z) = az + bz and a z + b z = 2 z 2 . az + bz = 2z^2 . From the choices, this only occurs if both a a and b b equal z ; z ; that is, a z + b z = ( z ) ( z ) + ( z ) ( z ) = z 2 + z 2 = 2 z 2 . az + bz = (z)(z) + (z)(z) = z^2 + z^2 = 2z^2 .

0 Helpful 0 Interesting 0 Brilliant 1 Confused

( \text {If } b = 2z \text { , then the last option ( } a = b^2 \text {is possible as well. }

If x = z or y = z, then the third option (a = z - b) can be true as well.

Hence, we have at least 3 correct options for the current form of the question.

Zee Ell - 4 years, 8 months ago

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Jup there has to be stated that x,y and zijn are distinct.

Peter van der Linden - 4 years, 8 months ago

I had "must" rather than "could" but somehow it disappeared in editing. Thanks.

Jason Dyer Staff - 4 years, 8 months ago

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