I think you should not waste time in multiplication

Algebra Level 1

True or false:

1 + x + y + z + x y + y z + z x + x y z = ( 1 + x ) ( 1 + y ) ( 1 + z ) . 1+x+y+z+xy+yz+zx+xyz = (1+x)(1+y)(1+z) .

True False

Gautam Bhambhani by Gautam Bhambhani , 19, India

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1 solution

Kay Xspre
Dec 2, 2015

I actually do not waste time on multiplication, but instead using the Vieta's formulas to come up with an answer. To illustrate the point, I can do the expansion of the equation to ( 1 + x + y + x y ) ( 1 + z ) = 1 + ( x + y + z ) + ( x y + y z + z x ) + ( x y z ) (1+x+y+xy)(1+z) = 1+(x+y+z)+(xy+yz+zx)+(xyz)

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