Question

分解因式:①(x+z)(x-z)+y(y-2x),②(ax+by)²+(bx-ay)²;③2x²+7x-15,④2x²-

Answer 1

①

(x+z)(x-z)+y(y-2x)

=x²-z²+y²-2xy

=(x-y)²-z²

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

②

(ax+by)²+(bx-ay)²

=a²x²+2abxy+b²y²+b²x²-2abxy+a²y²

=a²(x²+y²)+b²(x²+y²)

=(x²+y²)(a²+b²)

③

2x²+7x-15

1 5

2 -3

2x²+7x-15=(x+5)(2x-3)

④

2x²-3x-5

1 1

2 -5

2x²-3x-5=(x+1)(2x-5)