Help with Algebra 2?????
2009-06-29 4:29 pm
Look at the equation y^10n-2y^5n+1 and determine if it fits one of the special cases ( difference of 2 squares, perfect square trinomial, sum of cubes, difference of cubes), and why or why not?
回答 (2)
2009-06-29 5:42 pm
✔ 最佳答案
Factorize.y^(10n) - 2y^(5n) + 1
= [y^(5n)]^2 - 2y^(5n) + 1
Let y^(5n) = x.
x^2 - 2x + 1
= x^2 - x - x + 1
= (x^2 - x) - (x - 1)
= x(x - 1) - 1(x - 1)
= (x - 1)(x - 1)
Change x into y^(5n).
[y^(5n) - 1][y^(5n) - 1]
= [y^(5n) - 1]^2
We can know that the EXPRESSION y^(10n) - 2y^(5n) + 1 is a perfect square trinomial.
2009-06-29 5:44 pm
Let x = y^5n, then x² = (y^5n)² = (y^10n), and the equation can be written as
x² - 2x + 1, and this can be factorised as
(x - 1)²
so it is a perfect-square trinomial.
x² - 2x + 1, and this can be factorised as
(x - 1)²
so it is a perfect-square trinomial.
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