Question

因式分解3x2+4xy-y2

实数范围内因式分解

Answer 1

3x2+4xy-y2
=3x²-(y²-4xy)
=3x²-(y²-4xy+4x²)+4x²
=7x²-(y-2x)²
=(√7x+y-2x)(√7x-y+2x)
=[(√7-2)x+y][(√7+2)x-y]

Answer 2

原式=3(x²+4xy/3-y²/3)
=3(x²+4xy/3+4y²/9-4y²/9-y²/3)

=3[(x-2y/3)²-7y²/9]

=3(x-2y/3+√7y/3)(x-2y/3-√7y/3)