Question

Rozłóż na czynniki wielomiany, stosując wzór na różnicę kwadratów dwóch wyrażeń:

a) W(x) = (2x-1)²-(x+3)²
b) W(x) = (6x-5)²-(3x+1)²
c) W(x) = (9x+7)²-(8x+1)²
d) W(x) = (5x-3)²-(6x-1)²

Answer 1

a) W(x) = (2x-1)²-(x+3)²=
(2x-1+x+3)(2x-1-x-3)=
(3x+2)(x-4)
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b) W(x) = (6x-5)²-(3x+1)²=
(6x-5+3x+1)(6x-5-3x-1)=
(9x-4)(3x-6)
________________________
c) W(x) = (9x+7)²-(8x+1)²=
(9x+7+8x+1)(9x+7-8x-1)=
(17x+8)(x+6)
____________________________
d) W(x) = (5x-3)²-(6x-1)²=
(5x-3+6x-1)(5x-3-6x+1)=
(11x-4)(-x-2)
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