Shelley
grade 12
student

these two questions are to be factored completely but i have no idea how to factor them

  1. (x-4y) 2 - 3(x-4y) - 4
  2. x 6 + y 6


Hi Shelley,

A great deal of algebra is pattern recognition. The ability to look at an expression and see a pattern. Not unlike hearing the first two bars of a song and recognizing what it is. In your first problem the key is to look at

(x-4y) 2 - 3(x-4y) - 4 and see z 2 - 3z - 4 That is you need to see (x-4y) as one chunk. Thus a solution might look like this.

Let z = x - 4y, then

(x-4y) 2 - 3(x-4y) - 4

= z 2 - 3z - 4

= (z - 4)(z + 1) But z = x - 4y and hence this is (x - 4y - 4)(x - 4y +1)

For the second problem you know how to factor a sum of cubes. But (x 2) 3 = x 6 and (y 2) 3 = x 6, and thus

x 6 + y 6 = (x 2) 3  + (y 2) 3  Let s = x 2 and t = y 2, substitute into the expression above, and factor as a sum of cubes.

Cheers,
Penny

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