[{"data":1,"prerenderedAt":214},["ShallowReactive",2],{"content-/algebraic-identity-a-plus-b-cubed":3,"all-pages-for-dir":203,"related-/algebraic-identity-a-plus-b-cubed":204,"og-image-/algebraic-identity-a-plus-b-cubed":213},{"id":4,"title":5,"body":6,"category":187,"concepts":187,"description":188,"extension":189,"meta":190,"navigation":191,"ogImage":187,"path":192,"project_name":187,"published":193,"publishedAt":194,"seo":195,"source":187,"stem":196,"tags":197,"todo":187,"unpublished":193,"updatedAt":187,"__hash__":202},"pages/2026-02/2026-02-06/algebraic-identity-a-plus-b-cubed.md","(a+b)³ の展開公式を3Dで理解する",{"type":7,"value":8,"toc":178},"minimark",[9,13,17,27,31,34,41,45,125,128,132,135,160,163],[10,11,5],"h1",{"id":12},"ab-の展開公式を3dで理解する",[14,15,16],"h2",{"id":16},"展開公式",[18,19,20],"pre",{},[21,22,26],"code",{"className":23},[24,25],"language-math","math-display","(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3",[28,29,30],"p",{},"この公式は、辺の長さが (a+b) の立方体を8つのブロックに分解することで幾何学的に理解できる。",[14,32,33],{"id":33},"インタラクティブツール",[28,35,36],{},[37,38,40],"a",{"href":39},"/cube-identity","→ (a+b)³ 3D ビジュアライザーを開く",[14,42,44],{"id":43},"_8つのブロック","8つのブロック",[46,47,48,67],"table",{},[49,50,51],"thead",{},[52,53,54,58,61,64],"tr",{},[55,56,57],"th",{},"項",[55,59,60],{},"形状",[55,62,63],{},"個数",[55,65,66],{},"説明",[68,69,70,85,99,112],"tbody",{},[52,71,72,76,79,82],{},[73,74,75],"td",{},"a³",[73,77,78],{},"a × a × a",[73,80,81],{},"1",[73,83,84],{},"辺 a の立方体",[52,86,87,90,93,96],{},[73,88,89],{},"a²b",[73,91,92],{},"a × a × b",[73,94,95],{},"3",[73,97,98],{},"2辺が a、1辺が b のスラブ",[52,100,101,104,107,109],{},[73,102,103],{},"ab²",[73,105,106],{},"a × b × b",[73,108,95],{},[73,110,111],{},"1辺が a、2辺が b のバー",[52,113,114,117,120,122],{},[73,115,116],{},"b³",[73,118,119],{},"b × b × b",[73,121,81],{},[73,123,124],{},"辺 b の立方体",[28,126,127],{},"合計 1 + 3 + 3 + 1 = 8 個のブロックで (a+b)³ の立方体が構成される。\nこの係数 1, 3, 3, 1 はパスカルの三角形の4段目に対応している。",[14,129,131],{"id":130},"なぜ係数が-1-3-3-1-なのか","なぜ係数が 1, 3, 3, 1 なのか",[28,133,134],{},"(a+b)³ = (a+b)(a+b)(a+b) を展開すると、各項は3つの括弧からそれぞれ a か b を選ぶ組み合わせで決まる。",[136,137,138,145,150,155],"ul",{},[139,140,141,144],"li",{},[142,143,75],"strong",{},": 3つとも a を選ぶ → C(3,0) = 1通り",[139,146,147,149],{},[142,148,89],{},": 2つで a、1つで b を選ぶ → C(3,1) = 3通り",[139,151,152,154],{},[142,153,103],{},": 1つで a、2つで b を選ぶ → C(3,2) = 3通り",[139,156,157,159],{},[142,158,116],{},": 3つとも b を選ぶ → C(3,3) = 1通り",[14,161,162],{"id":162},"技術メモ",[28,164,165,166,169,170,173,174,177],{},"このビジュアライザーは CSS 3D transforms のみで構築しており、Three.js のような外部3Dライブラリは使用していない。\nCSS の ",[21,167,168],{},"transform-style: preserve-3d"," と ",[21,171,172],{},"perspective"," を組み合わせ、各ブロックの6面を ",[21,175,176],{},"div"," 要素で描画している。",{"title":179,"searchDepth":180,"depth":180,"links":181},"",2,[182,183,184,185,186],{"id":16,"depth":180,"text":16},{"id":33,"depth":180,"text":33},{"id":43,"depth":180,"text":44},{"id":130,"depth":180,"text":131},{"id":162,"depth":180,"text":162},null,"CSS 3D transforms を使ったインタラクティブなビジュアライザーで (a+b)³ = a³ + 3a²b + 3ab² + b³ を視覚的に理解する","md",{},true,"/algebraic-identity-a-plus-b-cubed",false,"2026-02-06T00:00:00.000Z",{"title":5,"description":188},"2026-02/2026-02-06/algebraic-identity-a-plus-b-cubed",[198,199,200,201],"math","education","algebra","3d-visualization","3wJa9rMTtNAlwJLUFTe7lqEXiyN0B7iROk5dEpk6T-s",[],[205,209],{"title":206,"path":207,"publishedAt":208},"所得税の誤りやすい事例集をAIクイズに変換する設計メモ","/tax-error-cases-quiz-design","2026-03-11T00:00:00.000Z",{"title":210,"path":211,"publishedAt":212},"フィボナッチ数列100万番目を求めるアプローチ","/fibonacci-millionth","2025-12-19T00:00:00.000Z","https://log.eurekapu.com/og/blog/algebraic-identity-a-plus-b-cubed.png?v=2026-02-06T00%3A00%3A00.000Z&title=(a%2Bb)%C2%B3%20%E3%81%AE%E5%B1%95%E9%96%8B%E5%85%AC%E5%BC%8F%E3%82%923D%E3%81%A7%E7%90%86%E8%A7%A3%E3%81%99%E3%82%8B&author=Kei%20Komatsu&sig=bdbd4cde49f79825",1785654981468]