Question

PTĐTTNT
a/ 3x^2 + 6xy + 3y^2 - 3z^2

b/ xz + yz - 5. ( x + y )

c/ 3x^2 - 5x - 3xy + 5y

d/ x^2 + 4x - 1/25y^2 +4

Answer 1

a: \(3x^2+6xy+3y^2-3z^2\)

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

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

b: \(xy+yz-5\left(x+y\right)\)

=z(x+y)-5(x+y)

=(x+y)(z-5)

c: \(3x^2-5x-3xy+5y\)

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

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

d: \(x^2+4x-\dfrac{1}{25}y^2+4\)

\(=\left(x^2+4x+4\right)-\left(\dfrac{1}{5}y\right)^2\)

\(=\left(x+2\right)^2-\left(\dfrac{1}{5}y\right)^2\)

\(=\left(x+2+\dfrac{1}{5}y\right)\left(x+2-\dfrac{1}{5}y\right)\)