Question

把下列各式分解因式

（1）（x+y)²-16(x-y)²
(2)a²(a-b)²-b²(a+b)²
(3)(x+y+z)²-(x-y-z)²
(4)(x+y)²-14(x+y)+49
(5)a²b²-0.01
(6)x²y-2xy²+y³

Answer 1

（1）（x+y)²-16(x-y)²
=(x+y+4x-4y)(x+y-4x+4y)
=(5x-3y)(5y-3x)

(2)a²(a-b)²-b²(a+b)²
=[a(a-b)+b(a+b)][a(a-b)-b(a+b)]
=(a^2+b^2)(a^2-2ab-b^2)

(3)(x+y+z)²-(x-y-z)²
=(x+y+z+x-y-z)(x+y+z-x+y+z)
=4x(y+z)

(4)(x+y)²-14(x+y)+49
=(x+y-7)^2

(5)a²b²-0.01
=(ab-0.1)^2

(6)x²y-2xy²+y³
=y(x^2-2xy+y^2)
=y(x-y)^2