Question

Ma puteti ajuta ?

Efectuati calculele :
a) (x + 2 )(x^2-x+3)-(x+1)(x^2+2x-5)
b) (2x+1)(x^2-2x+4)-(x-3)(2x^2+x+3)
c)(x-3)(x^2-3x+2)-(x+3)(x^2-2x+3)
d)(2x-1)(-x^2+x-2)+(2x-3)(x^2-x+1)

Answer 1

Răspuns:

Explicație pas cu pas:

a) (x + 2 )(x²-x+3)-(x+1)(x²+2x-5) =

= x³-x²+3x+2x²-2x+6-x³-2x²+5x-x²-2x+5=

= x³-x³-x²+2x²-2x²-x²+3x-2x+5x-2x+6+5 =

= -2x²+4x+11

b) (2x+1)(x²-2x+4)-(x-3)(2x²+x+3) =

= 2x³-4x²+8x+x²-2x+4-2x³-x²-3x+6x²+3x+9=

= 2x³-2x³-4x²+x²-x²+6x²+8x-2x-3x+3x+4+9 =

= 2x²+6x+13

c) (x-3)(x²-3x+2)-(x+3)(x²-2x+3) =

= x³-3x²+2x-3x²+9x-6-x³+2x²-3x-3x²+6x-9=

= x³-x³-3x²-3x²+2x²-3x²+2x+9x-3x+6x-6-9=

= -7x²+14x-15

d) (2x-1)(-x²+x-2)+(2x-3)(x²-x+1) =

= -2x³+2x²-4x+x²-x+2+2x³-2x²+2x-3x²+3x-3 =

= -2x³+2x³+2x²+x²-2x²-3x² -4x-x+2x+3x+2-3 =

= -2x²-1

Answer 2

Răspuns:

a) (x + 2)(x²-x+3)-(x+1)(x²+2x-5) = -2x²+4x+11

b) (2x+1)(x²-2x+4)-(x-3)(2x²+x+3) = 2x²+6x+13

c) (x-3)(x²-3x+2)-(x+3)(x²-2x+3) = -7x²+14x-15

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

Explicație pas cu pas:

a)

(x + 2)(x²-x+3)-(x+1)(x²+2x-5) =

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

= x³+x²+x+6 -x³-2x²+5x - x²-2x+5

= -2x²+4x+11

b)

(2x+1)(x²-2x+4)-(x-3)(2x²+x+3) =

= 2x³-4x²+8x + x²-2x+4-(2x³+x²+3x - 6x²-3x-9)

= 2x³-3x²+6x+4 - (2x³-5x²-9)

= 2x³-3x²+6x+4 - 2x³+5x²+9

= 2x²+6x+13

c)

(x-3)(x²-3x+2)-(x+3)(x²-2x+3) =

= x³-3x²+2x -3x²+9x-6 - (x³-2x²+3x + 3x²-6x+9)

= x³-6x²+11x-6 - (x³+x²-3x+9)

= x³-6x²+11x-6 - x³-x²+3x-9

= -7x²+14x-15

d)

(2x-1)(-x²+x-2)+(2x-3)(x²-x+1) =

= -2x³+2x²-4x + x²-x+2 + 2x³-2x²+2x -3x²+3x-3

= -2x²-1