Răspuns:
a) \( (2x+3)^2 - (2x + 1)(2x - 1) \)
= \( (4x^2 + 12x + 9) - (4x^2 - 1) \)
= \( 4x^2 + 12x + 9 - 4x^2 + 1 \)
= \( 12x + 10 \)
= \( 2(6x + 5) \)
b) \( (x - 1)^2 + (x - 5)(x + 5) - 2(x^2 - 1) \)
= \( x^2 - 2x + 1 + (x^2 - 25) - 2x^2 + 2 \)
= \( x^2 - 2x + x^2 - 25 - 2x^2 + 1 + 2 \)
= \( -x^2 - 2x - 22 \)
c) \( (x + 1)(x - 2) - (x - 3)^2 + x(x - 2) \)
= \( (x^2 - 2x + x - 2) - (x^2 - 6x + 9) + (x^2 - 2x) \)
= \( x^2 - x - 2 - x^2 + 6x - 9 + x^2 - 2x \)
= \( x^2 - x^2 + x^2 - x - 2x - 2x + 6x - 9 \)
= \( 3x - 9 \)
d) \( (2x - 5)^2 - (2x - 3)(2x + 3) \)
= \( (4x^2 - 20x + 25) - (4x^2 - 9) \)
= \( 4x^2 - 20x + 25 - 4x^2 + 9 \)
= \( -20x + 25 + 9 \)
= \( -20x + 34 \)
= \( 2(17 - 10x) \)
e) \( (x + 2)(x + 3) + (x - 3)^2 + (3x + 1)(3x - 1) \)
= \( x^2 + 5x + 6 + (x^2 - 6x + 9) + (9x^2 - 1) \)
= \( x^2 + 5x + 6 + x^2 - 6x + 9 + 9x^2 - 1 \)
= \( x^2 + x^2 + 9x^2 + 5x - 6x + 6 + 9 - 1 \)
= \( 11x^2 - x + 14 \)
f) \( (1 - 2x)^2 + (1 - 3x)^2 - (1 - 2x)(1 - 3x) \)
= \( (1 - 4x + 4x^2) + (1 - 6x + 9x^2) - (1 - 5x + 6x^2) \)
= \( 1 - 4x + 4x^2 + 1 - 6x + 9x^2 - 1 + 5x - 6x^2 \)
= \( 4x^2 - 6x + 1 + 9x^2 - 4x^2 + 5x - 6x^2 + 1 \)
= \( 9x^2 - 6x^2 - 4x + 5x + 1 + 1 \)
= \( 3x^2 - x + 2 \)
g) \( (5x - 2)^2 - (2 - 3x)^2 - (4x - 3)(4x + 3) \)
= \( (25x^2 - 20x + 4) - (4 - 12x + 9x^2) - (16x^2 - 9) \)
= \( 25x^2 - 20x + 4 - 4 + 12x - 9x^2 - 16x^2 + 9 \)
= \( 25x^2 - 9x^2 - 16x^2 - 20x + 12x + 4 - 4 + 9 \)
= \( 0 - 13x^2 - 8x + 9 \)
= \( -13x^2 - 8x + 9 \
^ înseamnă la putere
și fara /
