Question

1) Rút gọn

(2x-1) ²+(3x+1) ²+2(2x-1) (3x+1) 

2) Phân tích đa thức thành nhân tử : 4x⁴+1

Answer 1

1 )

\(\left(2x-1\right)^2+\left(3x+1\right)^2+2\left(2x-1\right)\left(3x+1\right)=\left[\left(2x-1\right)+\left(3x+1\right)\right]^2=\left(5x\right)^2=25x^2\)

2 ) 

\(4x^4+1=\left(2x^2\right)^2+2.2x^2.1+1-4x^2=\left(2x^2+1\right)^2-\left(2x\right)^2=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)

Answer 2

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

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

\(=\left(5x\right)^2=25x^2\)

Answer 3

1) (2x-1)²  + (3x+1)² +2(2x-1)(3x+1)

=(2x-1+3x+1)²

=(5x)²=25x²

2)4x⁴ +1 =(4x⁴ +4x² +1) -4x² =(2x² +1)² -4x² =(2x² +1 -2x)(2x²+1+2x)

Answer 4

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

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

\(=\left(5x\right)^2=25x^2\)

2. \(4x^4+1=\left(2x\right)^2+2.2x^2.1+1-4x^2=\left(2x^2-1^2\right)-\left(2x\right)^2=\left(2x^2-2x+1\right)\left(2x^2+2x+1\right)\)