Question

Wykonaj mnożenie i przeprowadź redukcję wyrazów podobnych.

(x+1)(x+2)(x+3) =

(2x+3)(3x+4)(4x+5)=

(x+1)(x²+1)(x³+1)=

(1-t)(1+t)(1+t²)(1+t⁴)=

(a²-b²)(a-b)(a+b)=

(2-t)(2+t)(3-t)(3+t)=

Z góry dzięuje!!! :) Daje najj! :))

Answer 1

(x+1)(x+2)(x+3) = (x²+2x+x+2)(x+3) = x³+3x²+2x²+6x+x²+3x+2x+6 =
= x³+6x²+11x+6

(2x+3)(3x+4)(4x+5)= (6x²+8x+9x+12)(4x+5) = 24x³+30x²+32x²+40x+36x²+45x+48x+70 =
=24x³+98x²+133x +70

(x+1)(x²+1)(x³+1)= (x³+x+x²+1)(x³+1)= x⁶+x³+x⁴+x+x⁵+x²+x³+1 =
= x⁶+x⁵+x⁴+2x³+x² +x+1

(1-t)(1+t)(1+t²)(1+t⁴)=(1-t²)(1+t²)(1+t⁴) = (1-t⁴)(1+t⁴) = 1-t⁸ (tu można było wykorzystać wzór skróconego mnożenia

(a²-b²)(a-b)(a+b)=(a²-b²)(a²-b²) = a⁴-a²b²-a²b²+b⁴ =
=a⁴ -2a²b² +b⁴

(2-t)(2+t)(3-t)(3+t)= (4-t²)(9-t²) = 36-4t²-9t²+t⁴ =
= 36 - 13t²+ t⁴