Номер 1:
а) 4x^2+8x =4x(x+2)
b) 3m-6n+mn-2n^2 = ((3m-6n)+(mn-2n^2)) = (3(m-2n)+n(m-2n) =(3+n)(m-2y)
B)9a^2-16=(3a+4)(3a-4)
g) y^3+18y^2+81y= y(y^2)+y(18y)+y(81) =y(y^2+18y+81) = y(y^2+9y+9y+81) =y((y^2+9y)+(9y+81)) = y(y(y+9)+9(y+9)= y(y+9)(y+9) =y(y+9)^2
Номер 2:
a) 36-a^2/18+3a=(6+a)(6-a)/3*(6+a)= 6-a/3=? 6/3 - a/3 => 2-a/3
b) 9p^2-q^2/9p^2+6pq+q^2= (3p+q)(3p-q)/3^2p^2+6pq+q^2 => (3p+q)(3p-q)/(3p+q)^2=> 3p-q/3p+q
Номер 3:
x^3-36x=0
x(x+6)(x-6)=0
x=0 x+6=0 x-6=0
x=0 x=-6 x=6
Ответ: x=0;-6;6
Номер 4:
x^2+14x+48=(x+8)(x+6)
x^2+14x+48=x^2+6x+8x+48
x^2+14x+48=x^2+14x+48
x^2+14x+48-x^2=14x+48
x^2+14x+48-x^2-14x=48
14x+48+0-14x=48
14x+0+48-14x=48
14x+48-14x=48
14x-14x+48=48
48=48
Тождество доказано.
Номер 5:
169^3+59^3/228 -169*59 =5032188/228 - 169*59 = 22071-169*59 =22071-9971 =12100