SIMPLE ALGEBRA?!? Challenge Problem...?

Question

(subtract x from a to z and get the product):

(x-a)(x-b)(x-c)...(x-z)=?

easy...

Answer 1

Is ZERO because the factor (x-x)=0 and all the product multiplie by zero gives zero.

Answer 2

do exactly what's asked. it incredibly is gruesome, yet no longer that gruesome: ?[(x+4)^2+y^2] + ?[(x-4)^2+y^2] = 10 ?[(x+4)^2+y^2] = 10 - ?[(x-4)^2+y^2] ... after subtracting ?[(x-4)^2+y^2] from the two sides. it quite is the "transpose". (x+4)^2 + y^2 = (10 - ?[(x-4)^2+y^2]) ^2 (x+4)^2 + y^2 = a hundred - 20?[(x-4)^2+y^2] + [(x-4)^2 + y^2] ...after squaring the two sides and FOIL on the suited it incredibly is all you asked for, yet it incredibly is basically 0.5 thank you to removing the radicals. First, simplify the effect above (which must be achieved besides): (x+4)^2 + y^2 - [(x-4)^2 + y^2] - a hundred = -20?[(x-4)^2+y^2] (x^2 + 8x + sixteen + y^2) - (x^2 - 8x + sixteen + y^2) - a hundred = -20?[(x-4)^2+y^2] 16x - a hundred = -20?[(x-4)^2+y^2] 4x - 25 = -5?[(x-4)^2+y^2] thankfully, each and all the squared words vanished on the left. Now sq. the two sides and simplify: 16x^2 - 200x + 625 = 25(x-4)^2 + 25y^2 16x^2 - 200x + 625 = 25x^2 - 200x + 4 hundred + 25y^2 225 = 9x^2 + 25y^2 it incredibly is so a techniques as you should flow, even nevertheless it may desire to be clever to observe that it incredibly is an ellipse well-known on the inspiration. That finally leads to a correctness examine, because of the fact the unique left area became the sum of two distance formulation calculations: the gap from (-4,0) to (x,y) and the gap from (4,0) to x,y. The set (or locus) of all factors the place the sum of the distances from 2 given factors (foci) are a hard and fast fee (10 subsequently) is one definition of an ellipse. considering that "first theory" ellipse has foci at (-4,0) and (4,0), it could be well-known on the inspiration with it incredibly is substantial axis on the x-axis. Divide the final equation via 225 on the two sides to get: a million = (x/5)^2 + (y/3)^2 and you spot that the intercepts are (-5,0), (5,0), (0,3) and (0,-3). and it incredibly is person-friendly to work out that the distances from the foci upload as much as ten for each of those factors on the ellipse. (Use the three-4-5 suited triangle ratios to right away get (3,0) is 5 far flung from each and each concentration.)

Answer 3

That's not algebra. A real mathematician would never jump to conclusions about what variables there are, merely based on a few. Try this. What fills the blank: _, a, b, c?

Answer 4

Since (x-x) is one of the products, the answer is surely = 0

Answer 5

Zero as (x-x) reduces the product to zero

Answer 6

um 0?
eventually you will hit (x-x) which equals 0, and 0 times anything = 0

Answer 7

0
cause there is x-x and that makes the ans 0

Answer 8

x to the 26th - abcdefghijklmnopqrstuvwxyz?

Answer 9

who cares?

Answer 10

ZERO ! ! !