Question

19. Efectuați calculele:
a) (3x + 2)(x²+2x-7)-(x-2)(2x² - 5x + 3);
b) (3x-4)(2x²-5x + 2) - (2x - 3)(x²-x+9);
c) (2x - 3)(x² - 2x + 5) - (x+3)(2x² - 4x + 1);
d) (5x-2)(x² - 2x + 3) - (x + 1)(5x²-3x + 2);
e) (x-3)(x+4)-(x-6)(x + 2) + (x+3)(x + 2)
Va rog multtt

Answer 1

Răspuns:

Explicație pas cu pas:

a) (3x + 2)(x²+2x-7)-(x-2)(2x² - 5x + 3) =

= (3x³+6x²-21x+2x²+4x-14) - (2x³-5x²+3x-4x²+10x-6) =

= 3x³-2x³+6x²+2x²+5x²+4x²-21x+4x-3x-10x-14+6 =

= x³+17x²-30x-8

b) (3x-4)(2x²-5x + 2) - (2x - 3)(x²-x+9) =

= (6x³-15x²+6x-8x²+20x-8) - (2x³-2x²+18x-3x²+3x-27) =

= 6x³-2x³-15x²-8x²+2x²+3x²+6x+20x-18x-3x-8+27 =

= 4x³-18x²+5x+19

c) (2x - 3)(x² - 2x + 5) - (x+3)(2x² - 4x + 1)=

= (2x³-4x²+10x-3x²+6x-15) - (2x³-4x²+x+6x²-12x+3) =

= 2x³-2x³-4x²-3x²+4x²-6x²+10x+6x-x+12x-15-3 =

= -9x²+27x-18

d) (5x-2)(x² - 2x + 3) - (x + 1)(5x²-3x + 2) =

= (5x³-10x²+15x-2x²+4x-6)-(5x³-3x²+2x+5x²-3x+2) =

= 5x³-5x³-10x²-2x²+3x²-5x²+15x+4x-2x+3x-6-2 =

= -14x²+20x-8

e) (x-3)(x+4)-(x-6)(x + 2) + (x+3)(x + 2) =

= (x²+4x-3x-12)-(x²+2x-6x-12) + (x²+2x+3x+6) =

= x²-x²+x²+x+4x+5x-12+12+6 = x²+10x+6

Answer 2

Explicație pas cu pas:

a) (3x + 2)(x²+2x-7)-(x-2)(2x² - 5x + 3) = 3x³ + 6x² - 21x + 2x² + 4x - 14 - (2x³ - 5x² + 3x - 4x² + 10x - 6) = 3x³+ 8x² - 17x - 14 - 2x³ + 9x² - 13x + 6 = x³ + 17x² - 30x - 8

b) (3x-4)(2x²-5x + 2) - (2x - 3)(x²-x+9) = 6x³ - 15x² + 6x - 8x² + 20x - 8 - (2x³ - 2x² + 18x - 3x² + 3x - 27) = 6x³ - 23x² + 26x - 8 - 2x³ + 5x² - 21x + 27 = 4x³ - 18x² + 5x + 19

c) (2x - 3)(x² - 2x + 5) - (x+3)(2x² - 4x + 1) = 2x³ - 4x² + 10x - 3x² + 6x - 15 - (2x³ - 4x² + x + 6x² - 12x + 3) = 2x³ - 7x² + 16x - 15 - 2x³ - 2x² + 11x - 3 = -9x² + 27x - 18

d) (5x-2)(x² - 2x + 3) - (x + 1)(5x²-3x + 2) = 5x³ - 10x² + 15x - 2x² + 4x - 6 - (5x³ - 3x² + 2x + 5x² - 3x + 2) = 5x³ - 12x² + 19x - 6 - 5x³ - 2x² + x - 2 = - 14x² + 20x - 8

e) (x-3)(x+4)-(x-6)(x + 2) + (x+3)(x + 2) = x² + 4x - 3x - 12 - (x² + 2x - 6x - 12) + x² + 2x + 3x + 6 = x² + x - 12 - x² + 4x + 12 + x² + 5x + 6 = x² + 10x + 6