Question

(x+y)²-4(x²-y²)+4(x-y)²如何分解

Answer 1

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

Answer 2

原式=(x+y)²-4(x+y)(x-y)+4(x-y)²
=[(x+y)-2(x-y)]²
=(3y-x)²

Answer 3

原式=x²+y²+2xy-4x²+4y²+4(x²-2xy+y²)
=x²+y²+2xy+8y²-8xy
=x²-6xy+9y²
=(x-3y)²

Answer 4

(x+y)²-4(x²-y²)+4(x-y)²
=x²+2xy+y²-4x²+4y²+4（x²-2xy+y²）
=x²+2xy+y²-4x²+4y²+4x²-8xy+4y²
=x²-6xy+9y²
=（x-3y)²