利用乘法公式因式分解下列各式 1.x^6-y^6 2.9x^4+5x^2+1?
回答 (2)
2016-03-27 3:02 pm
✔ 最佳答案
1 x^6-y^6=(x^3)^2-(y^3)^2=(x^3+y^3)(x^3-y^3)=(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)2 9x^4+5x^2+1=9x^4+6x^2+1-x^2=(3x^2+1)^2-x^2=(3x^2+1+x)(3x^2+1-x)=(3x^2+x+1)(3x^2-x+1)
2016-04-10 8:28 am
1.
x^6-y^6
=(x^3-y^3)(x^3+y^3)
=(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)
=(x+y)(x-y)(x^2-xy+y^2)(x^2+xy+y^2)
2.
9x^4+5x^2+1
=9x^4+6x^2+1-x^2
=(3x^2+1)^2-x^2
=(3x^2+1+x)(3x^2+1-x)
=(3x^2+x+1)(3x^2-x+1)
x^6-y^6
=(x^3-y^3)(x^3+y^3)
=(x+y)(x^2-xy+y^2)(x-y)(x^2+xy+y^2)
=(x+y)(x-y)(x^2-xy+y^2)(x^2+xy+y^2)
2.
9x^4+5x^2+1
=9x^4+6x^2+1-x^2
=(3x^2+1)^2-x^2
=(3x^2+1+x)(3x^2+1-x)
=(3x^2+x+1)(3x^2-x+1)
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