Question

Phân tích các đa thức sau thành nhân tử :

a) 49 . ( y - 4 )² - 9 . ( y + 3 )²

b) 4x⁸ + 1

c) 9. ( x + 1 )² -1

Answer 1

a) \(7^2\left(y-4\right)^2-3^2\left(y+3\right)^2=\left(7y-28\right)^2-\left(3y+9\right)^2\)

\(=\left(7y-28-3y-9\right)\left(7y-28+3y+9\right)=\left(4y-37\right)\left(10y-19\right)\)

b) \(\left(2x^4\right)^2+4x^4+1-4x^4\)

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

c) \(3^2\left(x+1\right)^2-1=\left(3x+3\right)^2-1=\left(3x+2\right)\left(3x+4\right)\)