Question

PTĐTTNT

a/ 1/2x^2 - 2y^2

b/ 3x^2 - 5x - 3y^2 + 5y

c/ 3x^2 - 7x - 6

d/ 49 - x^2 + 2xy - y^2

 

Answer 1

a) \(...=\dfrac{1}{2}\left(x^2-4y^2\right)=\dfrac{1}{2}\left(x-2y\right)\left(x+2y\right)\)

b) \(...=3\left(x^2-y^2\right)-5\left(x-y\right)=3\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)

\(=\left(x-y\right)\left(3x-3y-5\right)\)

c) \(...=3x^2+2x-9x-6=x\left(3x+2\right)-3\left(3x+2\right)=\left(3x+2\right)\left(x-3\right)\)

d) \(...=49-\left(x^2-2xy+y^2\right)=49-\left(x-y\right)^2=\left(7+x-y\right)\left(7-x+y\right)\)

Answer 2

$a)$ $1/2 x^2 - 2y^2$

$= 2(1/4 x^2 - y^2)$

$= 2(1/2 x - y)(1/2 x + y)$

$b)$ $3x^2 - 5x - 3y^2 + 5y$

$= (3x^2 - 3y^2) - (5x- 5y)$

$= 3(x^2 - y^2) - 5(x - y)$

$= 3(x-y)(x+y) - 5(x-y)$

$= (x-y)[3(x+y) - 5]$

$= (x-y)(3x+3y-5)$

$c)$ $3x^2 - 7x - 6$

$= 3x^2 - 9x + 2x - 6$

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

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

$d)$ $49 - x^2 + 2xy - y^2$

$= 49 - (x^2 - 2xy + y^2)$

$= 7^2 - (x - y)^2$

$= (7 - x + y)(7 + x - y)$