A=x+y B=x-y
(1)A+B
=(x+y)+(x-y)
=2x
(2)AB
=(x+y)(x-y)
=x²-xy
+xy-y²
=x²-y²
(3)A²-B²
=(A+B)(A-B)
=[(x+y)+(x-y)][(x+y)-(x-y)]
=2x × 2y
=4xy
(4)A²+B²
=(x+y)²+(x-y)²
=x²+2xy+y²+x²-2xy+y²
=2x²+2y²
こんな感じでしょうか。
A=x+y B=x-y
(1)A+B
=(x+y)+(x-y)
=2x
(2)AB
=(x+y)(x-y)
=x²-xy
+xy-y²
=x²-y²
(3)A²-B²
=(A+B)(A-B)
=[(x+y)+(x-y)][(x+y)-(x-y)]
=2x × 2y
=4xy
(4)A²+B²
=(x+y)²+(x-y)²
=x²+2xy+y²+x²-2xy+y²
=2x²+2y²
こんな感じでしょうか。
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