Question

数学一道式子化简的题目，有答案求详细过程

请问红线那里是怎么化简的，怎么变成第二个式子的，有什么规律吗

Answer 1

1–(3x–4x³)²=(1–3x＋4x³)(1＋3x–4x³)
=[4(x³＋1)–3(x＋1)][–4(x³–1)＋3(x–1)]
=[4(x＋1)(x²–x＋1)–3(x＋1)][–4(x–1)(x²＋x＋1)＋3(x–1)]
=(x＋1)(4x²–4x＋1)(x–1)(–4x²–4x–1)
=–(x＋1)(2x–1)²(x–1)(2x＋1)²
=(1–x²)(4x²–1)²

Answer 2

(3-12x^2)/√[1-(3x-4x^3)^2]
=3(1-4x^2)/√(1-9x^2+24x^4-16x^6)
=3(1-4x^2)/√[(1-x^2-8x^2+24x^4-16x^6)]
=3(1-4x^2)/√[1-x^2-8x^2(1-3x^2+2x^4)]
=3(1-4x^2)/√[(1-x^2)-8x^2(1-2x^2)(1-x^2)]
=3(1-4x^2)/√[(1-x^2)(1-8x^2+16x^4)]
=3(1-4x^2)/√[(1-x^2)(1-4x^2)^2]

Answer 3

1–(3x–4x³)²
=(1–3x＋4x³)(1＋3x–4x³)
=[4(x³＋1)–3(x＋1)][–4(x³–1)＋3(x–1)]
=[4(x＋1)(x²–x＋1)–3(x＋1)][–4(x–1)(x²＋x＋1)＋3(x–1)]
=(x＋1)(4x²–4x＋1)(x–1)(–4x²–4x–1)
=–(x＋1)(2x–1)²(x–1)(2x＋1)²
=(1–x²)(4x²–1)²