Question

なゆ

カッコ4を教えてください🙇‍♀️

次の式を因数分解せよ。
(1) (x+y)2-4(x+y) +3
(3)(x+y+z)(x+3y+z)-8y2
(2)9a2-62-4bc-4c2
(4)(x-y)+(y-z) 3

Answer 1

あ

a³+b³=(a+b)(a²-ab+b²)なので
(x-y)³+(y-z)³
={(x-y)+(y-z)}{(x-y)²-(x-y)(y-z)+(y-z)²}
=(x-z){(x²-2xy+y²)-(xy-xz-y²+yz)+(y²-2yz+z²)}
=(x-z)(x²-3xy+xz+3y²-3yz+z²)

=(x-z)1/2(2x²-6xy+2xz+6y²-6yz+2z²)
=1/2(x-z){(x²-6xy+9y²)+(x²+2xz+z²)+(9y²-6yz+z²)-12y²}
=1/2(x-z){(x-3y)²+(x+z)²+(3y-z)²-12y²}