Question

Phân tích đa thức thành nhan tử:

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

Answer 1

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

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

\(=2x.\left(4x+2\right)\)

\(=8x^2+4x\).

Answer 2

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

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

\(=2x\left(4x+2\right)=4x\left(2x+1\right)\)

Answer 3

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

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

\(=2x\left(4x+2\right)\)

\(=4\left(x^2+x\right)\).

Answer 4

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

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

\(=2x\left(4x+2\right)\)

\(=4x\left(2x+1\right)\)

\(=4\left(2x^2+x\right)\)

Answer 5

(3x + 1)² - (x + 1)²

<=> = (3x² + 2.3x + 1) - (x² + 2.2x + 1)

<=> = 3x² + 6x + 1 - x² - 4x -1

<=> = 3x² - x² + 6x - 4x + 1 -1

<=> = 2x² + 2x

<=> = 2x.(x + 1)

Answer 6

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

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

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

\(=2x\left(4x+2\right)=8x^2+4x\)