数学题在线解答a^4+b^4+(a+b)^4运作拆项或添项分解因式
2019-05-27
数学题在线解答a^4+b^4+(a+b)^4运作拆项或添项分解因式
优质解答
a^4+b^4+(a+b)^4
=a^4＋b^4＋[(a＋b)²]²
=a^4＋b^4＋(a²＋2ab＋b²)²
=a^4＋b^4＋[(a²＋b²)＋2ab]²
=a^4＋b^4＋(a²＋b²)²＋2×2ab(a²＋b²)＋(2ab)²
=a^4＋b^4＋a^4＋2a²b²＋b^4＋4a³b＋4ab³＋4a²b²
=(2a^4＋2b^4＋4a²b²)＋（4a³b＋4ab³）＋2a²b²
=2（a²＋b²）²＋4ab(a²＋b²)＋2a²b²
=2[（a²＋b²）²＋2ab(a²＋b²)＋(ab)²]
=2(a²＋b²＋ab)²
a^4+b^4+(a+b)^4
=a^4＋b^4＋[(a＋b)²]²
=a^4＋b^4＋(a²＋2ab＋b²)²
=a^4＋b^4＋[(a²＋b²)＋2ab]²
=a^4＋b^4＋(a²＋b²)²＋2×2ab(a²＋b²)＋(2ab)²
=a^4＋b^4＋a^4＋2a²b²＋b^4＋4a³b＋4ab³＋4a²b²
=(2a^4＋2b^4＋4a²b²)＋（4a³b＋4ab³）＋2a²b²
=2（a²＋b²）²＋4ab(a²＋b²)＋2a²b²
=2[（a²＋b²）²＋2ab(a²＋b²)＋(ab)²]
=2(a²＋b²＋ab)²