1. Descompuneți:
a) (3x - 1)2 -9;
c) (x - 4x + 4) - 9y2;
e) (2x + 5)(3x - 1) - 4(2x + 5);
b) 49x2 - 100;
d) (1 + 4x + 4.x?) - 25;
f) (3x - 2)(x + 7) + (3x - 2)(x - 5).
Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
(A)
(3x - 1)² - 9 = (3x - 1)² - 3² =
[(3x - 1) - 3]·[(3x - 1) + 3] =
(3x - 1 - 3)·(3x - 1+ 3) = (3x - 4)·(3x +2)
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(B) 49x² - 100 = (7x)² - 10² =
(7x - 10) · (7x + 10)
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(C) (x - 4x + 4) - 9y² = (x - 2)² - (3y)² =
[(x - 2) - 3y]·[(x - 2) + 3y] =
(x - 2 - 3y) · (x - 2 + 3y)
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(D) (1 + 4x + 4·x²) - 25 = (1 + 2x)² - 5² =
[(1 + 2x) - 5] ·[(1 + 2x) + 5] =
(1 + 2x - 5) · (1 + 2x + 5) =
(2x - 4) · (6 + 2x) = 2 · (x - 2) · 2 · (3 + x) =
4 · (x - 2) · (3 + x)
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(E) (2x + 5)(3x - 1) - 4(2x + 5) = (2x + 5) · [(3x - 1) - 4] =
(2x + 5) · (3x - 1 - 4) = (2x + 5) · (3x - 5)
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(F) (3x - 2)(x + 7) + (3x - 2)(x - 5) =
(3x - 2) · [(x + 7) + (x - 5)] =
(3x - 2) · (x + 7 + x - 5) =
(3x - 2) · (2x + 2) = 2 · (3x - 2) · (x + 1)
==pav38==