Question

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Answer 1

Bài 5:

1: \(A=x^3-3x^2+3x+1012\)

\(=x^3-3x^2+3x-1+1013\)

\(=\left(x-1\right)^3+1013\)

Khi x=11 thì \(A=\left(11-1\right)^3+1013=10^3+1013=1000+1013=2013\)

2: \(B=x^3-6x^2+12x-108\)

\(=x^3-6x^2+12x-8-100\)

\(=\left(x-2\right)^3-100\)

Khi x=12 thì \(B=\left(12-2\right)^3-100=10^3-100\)

=1000-100

=900

Bài 4:

1: \(\left(x+1\right)^3-\left(x-4\right)\left(x+4\right)-x^3\)

\(=x^3+3x^2+3x+1-\left(x^2-16\right)-x^3\)

\(=3x^2+3x+1-x^2+16=2x^2+3x+17\)

2: \(\left(x+2\right)^3-x\left(x+3\right)\left(x-3\right)-12x^2-8\)

\(=x^3+6x^2+12x+8-x\left(x^2-9\right)-12x^2-8\)

\(=x^3-6x^2+12x-x^3+9x=-6x^2+21x\)

Bài 3:

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

\(=x^3-6x^2+12x-8+x^3+6x^2+12x+8\)

\(=2x^3+24x\)

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

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

\(=x^3-3x^2+3x-1-x^3-3x^2-3x-1=-6x^2-2\)

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

\(=-x^3+3x^2-3x+1+x^3+9x^2+27x+27\)

\(=12x^2+24x+28\)

Bài 2:

1: \(x^3-6x^2+12x-8\)

\(=x^3-3\cdot x^2\cdot2+3\cdot x\cdot2^2-2^3\)

\(=\left(x-2\right)^3\)

2: \(x^3-9x^2+27x-27\)

\(=x^3-3\cdot x^2\cdot3+3\cdot x\cdot3^2-3^3\)

\(=\left(x-3\right)^3\)

3: \(-x^3+9x^2-27x+27\)

\(=\left(-x\right)^3+3\cdot\left(-x\right)^2\cdot3+3\cdot\left(-x\right)\cdot3^2+3^3\)

\(=\left(-x+3\right)^3\)

Bài 1:

1: \(\left(x+3\right)^3=x^3+3\cdot x^2\cdot3+3\cdot x\cdot3^2+3^3\)

\(=x^3+9x^2+27x+27\)

2: \(\left(x+1\right)^3=x^3+3\cdot x^2\cdot1+3\cdot x\cdot1^2+1^3\)

\(=x^3+3x^2+3x+1\)

3: \(\left(2-x\right)^3=2^3-3\cdot2^2\cdot x+3\cdot2\cdot x^2-x^3\)

\(=8-12x+6x^2-x^3\)

4: \(\left(x-3\right)^3=x^3-3\cdot x^2\cdot3+3\cdot x\cdot3^2-3^3\)

\(=x^3-9x^2+27x-27\)

5: \(\left(2x+1\right)^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1+3\cdot2x\cdot1^2+1^3\)

\(=8x^3+12x^2+6x+1\)

6: \(\left(3x+2\right)^3=\left(3x\right)^3+3\cdot\left(3x\right)^2\cdot2+3\cdot3x\cdot2^2+2^3\)

\(=27x^3+54x^2+36x+8\)

7: \(\left(2x-3\right)^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot3+3\cdot2x\cdot3^2-3^3\)

\(=8x^3-36x^2+54x-27\)

8: \(\left(3x-1\right)^3=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot1+3\cdot3x\cdot1^2-1^3\)

\(=27x^3-27x^2+9x-1\)