Question

1) (x+1)³ +(x-1)³ +x³-3x(x+1)(x-1)

2) (a+b+c)²+(a+b-c)² +(2a-b)²

3)100²-99²+98²-97² +...+ 2²-1²

4) 3(2²+1)(2⁴+1)....(2⁶⁴+1)+1

5) (a+b+c)²+(a+b-c)²-2(a+b)²

các bạn làm được câu nào thì làm giúp mink mai mink nộp rồi

Answer 1

1: \(=x^3+3x^2+3x+1+x^3-3x^2+3x-1+x^3-3x\left(x^2-1\right)\)

\(=3x^3+6x-3x^3+3x\)

\(=9x\)

2: \(=2\left(a+b\right)^2+2c^2+4a^2-4ab+b^2\)

\(=2a^2+4ab+2b^2+2c^2+4a^2-4ab+b^2\)

\(=6a^2+3b^2+2c^2\)

3: =100+99+98+...+2+1

=5050

4: \(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\cdot...\cdot\left(2^{64}+1\right)+1\)

\(=\left(2^4-1\right)\left(2^4+1\right)\cdot...\cdot\left(2^{64}+1\right)+1\)

\(=2^{128}-1+1=2^{128}\)