A) Выражение: 49*(5*a-1)^2-35*a^2
Ответ: 1190*a^2-490*a+49
Решаем по действиям:1. (5*a-1)^2=25*a^2-10*a+1
(5*a-1)^2=((5*a-1)*(5*a-1)) 1.1.
(5*a-1)*(5*a-1)=25*a^2-10*a+1
(5*a-1)*(5*a-1)=5*a*5*a-5*a*1-1*5*a+1*1
a*a=a^2
a*a=a^(1+1)
-5*a-5*a=-10*a2.
49*(25*a^2-10*a+1)=1225*a^2-490*a+49
49*(25*a^2-10*a+1)=49*25*a^2-49*10*a+49*1 2.1.
49*25=1225
9*10=490
4903. 1225*a^2-35*a^2=1190*a^2
b)Выражение: (x+y)^3+(x-y)^3
Ответ: 2*x^3+6*x*y^2
Решаем по действиям:1.
(x+y)^3=x^3+3*x^2*y+3*x*y^2+y^3
(x+y)^3=((x+y)*(x+y)*(x+y))
(x+y)*(x+y)=x^2+2*x*y+y^2
(x+y)*(x+y)=x*x+x*y+y*x+y*y
x*x=x^2
x*x=x^(1+1)
x*y+y*x=2*x*y
y*y=y^2
y*y=y^(1+1)
(x^2+2*x*y+y^2)*(x+y)=x^3+3*x^2*y+3*x*y^2+y^3
(x^2+2*x*y+y^2)*(x+y)=x^2*x+x^2*y+2*x*y*x+2*x*y*y+y^2*x+y^2*y
x^2*x=x^3
x^2*x=x^(2+1)
x*x=x^2
x*x=x^(1+1)
x^2*y+2*x^2*y=3*x^2*y
y*y=y^2
y*y=y^(1+1)
2*x*y^2+y^2*x=3*x*y^2
y^2*y=y^3
y^2*y=y^(2+1)
(x-y)^3=x^3-3*x^2*y+3*x*y^2-y^3 (x-y)^3=((x-y)*(x-y)*(x-y)) 2.1. (x-y)*(x-y)=x^2-2*x*y+y^2
(x-y)*(x-y)=x*x-x*y-y*x+y*y
x*x=x^2
x*x=x^(1+1) 2.1.1.1. 1+1=2
-x*y-y*x=-2*x*y
y*y=y^2
y*y=y^(1+1)
(x^2-2*x*y+y^2)*(x-y)=x^3-3*x^2*y+3*x*y^2-y^3 (x^2-2*x*y+y^2)*(x-y)=x^2*x-x^2*y-2*x*y*x+2*x*y*y+y^2*x-y^2*y 2.2.1. x^2*x=x^3 x^2*x=x^(2+1)
x*x=x^2
x*x=x^(1+1)
-x^2*y-2*x^2*y=-3*x^2*y
y*y=y^(1+1)
2*x*y^2+y^2*x=3*x*y^2
y^2*y=y^3
y^2*y=y^(2+1)
x^3+x^3=2*x^34. 3*x^2*y-3*x^2*y=05. 3*x*y^2+3*x*y^2=6*x*y^26. y^3-y^3=0
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