C = a 2 − a a + a + 1 − a 2 + a a − a + 1 + a + 1         ( D K : a ≥ 0 ) C = a ( a ) 3 − 1 a + a + 1 − a ( a ) 3 + 1 a − a + 1 + a + 1 = a ( a − 1 ) − a ( a + 1 ) + a + 1 = a − a − a − a + a + 1 = a - 1 2

Ta có:

aa = 10 a + a =11a

bbb = 100b + 10b + b =111b

abab = 1000a+10a+100b+b=1010a + 101b

aabb=1000a+100a+10b+b=1100a+11b

Đáp số:

a)a^2

b)b^3

c)a^2,b^2

d)a^2,b^2

(a+b-c)+(a+b)-(a-b-c)=a+b-c+a+b-a+b+c=2b

(a+b-c)+(a+b)-(a-b-c)=a+b-c+a+b-a+b+c=a+3b

\(\left(-a+b\right)-\left(b+c+a\right)+\left(c-a\right)\\ =-a+b-b-c-a+c-a\\ =-3a\)

a: =b-c-a+c+1-a-b+c

=-2a+1

b: =a-b-c-b+c+a+c-b-a

=c-3b+a

c: =2(a-b-b+c-c+a)

=2(2a-2b)

=4a-4b

a) \(\left(b-c\right)-\left(a-c-1\right)-\left(a+b-c\right)\)

\(=b-c-a+c+1-a-b+c\)

\(=c-2a+1\)

b) \(\left(a-b-c\right)-\left(b-c-a\right)+\left(c-b-a\right)\)

\(=a-b-c-b+c+a+c-b-a\)

\(=a-3b+c\)

c) \(2\cdot\left(a-b\right)-2\cdot\left(b-c\right)-2\cdot\left(c-a\right)\)

\(=2\cdot\left(a-b-b+c-c+a\right)\)

\(=2\cdot\left(2a-2b\right)\)

\(=4a-4b\)

=(b+c)(ac-a²+bc-ab)+(b+c)(ac-bc+a²-ab)+(c+a)(a+b)(b-c)

=(b+c)(ac-a²+bc-ab+ac-bc+a²-ab)+(a+c)(a+b)(b-c)

=(b+c)(2ac-2ab)-(a+c)(a+b)(c-b)

=(b+c).2a.(c-b)-(a²+ab+ac+bc)(c-b)

=(c-b)(2ab+2ac-a²-ab-ac-bc)

=(c-b)(-a²+ab+ac-bc)=(c-b)[a(b-a)-c(b-a)]

=(c-b)(b-a)(a-c)

Ta có: \(\left(b-c\right)^3+\left(c-a\right)^3-\left(a-b\right)^3-3\left(a-b\right)\left(b-c\right)\left(c-a\right)\)

\(=\left(b-c+c-a\right)\left[\left(b-c\right)^2-\left(b-c\right)\left(c-a\right)+\left(c-a\right)^2\right]-\left(a-b\right)\left[1+3\left(b-c\right)\left(c-a\right)\right]\)

\(=\left(b-a\right)\left(b^2-3bc+3c^2+ab-3ac+a^2\right)-\left(a-b\right)\left(1+3bc-3ab-3c^2+3ac\right)\)

\(=\left(b-a\right)\left(b^2-3bc+3c^2+ab-3ac+a^2+1+3bc-3ab-3c^2+3ac\right)\)

\(=\left(b-a\right)\left(b^2-2ab+a^2+1\right)\)

\(=\left(b-a\right)^3+\left(b-a\right)\)

\(=b^3-3b^2a+3ba^2-a^3+b-a\)

`#3107.101107`

`3(a + b)(a + c)(b + c)`

`= 3(a^2 + 2ab + bc)(b + c)`

`= 3(a^2b + a^2c + 2ab^2 + 2abc + b^2c + bc^2)`

`= 3a^2b + 3a^2c + 6ab^2 + 6abc + 3b^2c + 3bc^2`