Question

Phân tích đa thức thành nhân tử:

^{1) \(x^2+4x+4-9y^2\)}

2) \(x^2-2xy+y^2-16\)

Answer 1

1. x²+4x+4-9y²

= (x + 2)² - (3y)²

= ( x+ 2+ 3y) (x +2 -3y)

2. x² -2xy+y² -16

= (x - y)² - (4 )²

= ( x -y + 4) (x -y -4)

Answer 2

\(x^2+4x+4-9x^2\)

\(=\left(x^2+4x+4\right)-9y^2\)

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

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

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

\(x^2-2xy+y^2-16\)

\(=\left(x^2-2xy+y^2\right)-16\)

\(=\left(x^2-y^2\right)-4^2\)

\(=\left[\left(x-y\right)^2+4\right]\left[\left(x-y\right)^2-4\right]\)

\(=\left(x-y+4\right)\left(x-y-4\right)\)

Answer 3

a. \(\left(x+2\right)^2\) - \(\left(3y\right)^2\) = \(\left(x+2-3y\right)\)\(\left(x+2+3y\right)\)

Answer 4

1/x²+4x+4-9y²

= (x²+4x+4)-9y²

= (x+2)²-(3y)²

= [(x+2)-3y][(x+2)+3y]

= (x+2-3y)(x+2+3y)

2/x²-2xy+y²-16

= (x²-2xy+y²)-16

= (x-y)²-4²

= [(x-y)-4][(x-y)+4]

= (x-y-4)(x-y+4)