Question

2. (50 балів) спростити вираз:
1) (x-1)² - (x + 3)(x-3)
2) (2a-1)(4a² +2a+1)
3) (a-5 a² + 5a+25)-(a-1)a²+a+1)​

Answer 1

$\displaystyle\bf\\1)\\\\(x-1)^{2} -(x+3)(x-3)=x^{2} -2x+1-(x^{2} -9)=\\\\=x^{2} -2x+1-x^{2} +9=-2x+10\\\\2)\\\\(2a-1)(4a^{2} +2a+1)=(2a)^{3} -1^{3} =8a^{3} -1\\\\3)\\\\(a-5)(a^{2} +5a+25)-(a-1)(a^{2} +a+1)=\\\\=a^{3} -5^{3} -(a^{3} -1^{3} )=a^{3} -125-a^{3} +1=-124$