Question

Biến đổi vế trái thành vế phải : 

x(x+1)(x+2)(x+3)+1 = (x²+3x+1)²

Answer 1

\(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

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

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

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

\(=x^4+3x^3+2x^2+3x^3+9x^2+6x+1\)

\(=x^4+\left(3x^3+3x^3\right)+\left(2x^2+9x^2\right)+6x+1\)

\(=x^4+6x^3+11x^2+6x+1\)

\(=\left(x^2+3x+1\right)^2\) (Bằng vế phải)

Answer 2

\(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

\(=\left[x\left(x+3\right)\right]\left[\left(x+1\right)\left(x+2\right)\right]+1\)

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

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

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

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

Answer 3

Mk sửa lại dòng cuối nhé !

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

Answer 4

Ta biến đổi vế trái : 

      \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

\(=\left[x\left(x+3\right)\right]\left[\left(x+1\right)\left(x+2\right)\right]+1\)

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

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

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

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

Answer 5

Ta biến đổi vế trái : 

      \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)

\(=\left[x\left(x+3\right)\right]\left[\left(x+1\right)\left(x+2\right)\right]+1\)

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

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

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

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