二次三项式因式分解a^2-1+6a4x^4+x^2-3x^2-2ax-2a^22x^2-8xy+5y^2不一定要都做出来--

Question

二次三项式因式分解
a^2-1+6a
4x^4+x^2-3
x^2-2ax-2a^2
2x^2-8xy+5y^2
不一定要都做出来- -

Answer 1

a^2-1+6a
=(a+3)^2-10
=(a+3+√10)(a+3-√10)
4x^4+x^2-3
=(4x^2-3)(x^2+1)
=(2x+√3)(2x-√3)(x^2+1)
x^2-2ax-2a^2
=x^2-2ax+a^2-3a^2
=(x-a)^2-3a^2
=(x-a+√3a)(x-a-√3a)
2x^2-8xy+5y^2
=2(x^2-4xy+4y^2)-3y^2
=2(x-2y)^2-3y^2
=[√2(x-2y)-√3y][√2(x-2y)+√3y]
=[√2x-2√2y-√3y][√2x-2√2y+√3y]