Question

Działania na wielomianach a) (-x2+7x+2)(7-4x2-6x) b)7(4x3-5x2+3x-2)-5(-x2+7x+2)-x2+7x+2(7-4x2-6x) c)(2-x6-4x2)(x4-7x6-2) d) 2x3-1(-4x+5+x2-3x+1)

Answer 1

(-x2+7x+2)(7-4x2-6x)=-7x²+4x⁴+6x³+49x-32x³-42x²+14-8x²-12x=-57x²+4x⁴-26x³+49x+14

 

7(4x3-5x2+3x-2)-5(-x2+7x+2)-x2+7x+2(7-4x2-6x)=

28x³-35x²+21x-14+5x²-35x-10-x²+7x+14-8x²-12x=28x³-39x²-7x-10

 

(2-x6-4x2)(x4-7x6-2)=2x⁴-14x⁶-4-x¹⁰+7x¹²+2x⁶-4x⁶+28x⁸+8x²=2x⁴-16x⁶-4-x¹⁰+7x¹²+28x⁸+8x²

 

2x3-1(-4x+5+x2-3x+1)=2x³+4x-5-x²+3x-1=2x³+7x-6-x²

 

Answer 2

a) (-x^2 +7x +2)(7- 4x^2 -6x) = -7x^2 +4x^4 +6x^3 +49x -28x^3 -42x^2 +14 -8x^2 -12x =

     = -57x^2 +4x^4 -22x^3 +37x +14

 

b) 7(4x^3 -5x^2 +3x -2)-5(x^2 +7x +2)-x^2 +7x +2(7-4x^2 -6x) = 28x^3 -35x^2 +21x-14-

     -5x^2 -35x -10 -x^2 +7x +14 -8x^2 -12x = -28x^3 -49x^2 -19x +4

 

c)(2 -x^6 -4x^2)(x^4 -7x^6-2) =2x^4 -14x^6 -4 -x^10+7x^12 +2x^6 -4x^6 +28x^8+8x^2 =

   = 2x^4 -8x^6 -4 -x^10 +7x^12 +28x^8 +8x^2

 

d) 2x^3 -1(-4x +5 +x^2 -3x +1) = 2x^3 +4x-5 -x^2 +3x -1 = 2x^3 +7x -6 -x^2