Question

Phân tích thành nhân tử

a) 9x²+6xy+y²

b) 6x\(-\)9\(-\)x²

c) x²+4y²+4xy

d) (x\(-\)2y)²\(-\)(x+2y)²

Answer 1

a) $9x^2+6xy+y^2$

$=(3x)^2+2.3xy+y^2$

$=(3x+y)^2$

b) $6x-9-x^2$

$=-(x^2-6x+9)$

$=-(x-3)^2$

c) $x^2+4y^2+4xy$

$=x^2+(2y)^2+4xy$

$=(x+2y)^2$

d) $(x-2y)^2-(x+2y)^2$

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

$=-4y.2x=-8xy$

Answer 2

a, \(9x^2+6xy+y^2\)

\(=9x^2+3xy+3xy+y^2\)

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

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

b, \(6x-9-x^2\)

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

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

c, \(x^2+4y^2+4xy\)

\(=x^2+2xy+2xy+4y^2\)

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

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

d, \(\left(x-2y\right)^2-\left(x+2y\right)^2\)

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

\(=-8xy\)

Chúc bạn học tốt!!!