4道初2因式分解题第一道:X^2n+X^n-1/9y^2+1/4第二道:X^4-11x^2y^2+y^2第三道：(2x^2-3x+1)^2-22X^2+33X-1第四道：X^4+7X^3+14X^2+7X+1

Question

4道初2因式分解题
第一道:X^2n+X^n-1/9y^2+1/4
第二道:X^4-11x^2y^2+y^2
第三道：(2x^2-3x+1)^2-22X^2+33X-1
第四道：X^4+7X^3+14X^2+7X+1

Answer 1

1.
x^2n+x^n-1/9y^2+1/4
=(x^n)^2+(x^n)+1/4-(1/9)y^2
=[(x^n)^2+(x^n)+1/4]-(1/9)y^2
=[x^n+1/2]^2-[(1/3)y]^2
=[x^n+1/2+(1/3)y]*[x^n+1/2-(1/3)y]
2.
x^4-11x^2y^2+y^4
=x^4+(3x^3y-3x^2y)-[-x^2y^2-9x^2y^2-x^2y^2]+(3xy^3-3xy^3)+y^4
=(x^4+3x^3y-x^2y^2)+(-3x^3y-9x^2y^2+3xy^3)+(-x^2y^2-3xy^3+y^4)
=x^2(x^2+3xy-y^2)-3xy(x^2+3xy-y^2)-y^2(x^2+3xy-y^2)
=(x^2+3xy-y^2)(x^2-3xy-y^2)
3.
(2x^2-3x+1)^2-22x^2+33x-1
=(2x^2-3x+1)^2-22x^2+33x-11+10
=(2x^2-3x+1)^2-11(2x^2-3x+1)+10
=(2x^2-3x+1-1)(2x^2-3x+1-10)
=(2x^2-3x)(2x^2-3x-9)
=x(2x-3)(x-3)(2x+3)
4.x^4+7x^3+14x^2+7x+1
=x^4+7x^3+(12x^2+2x^2)+7x+1
=(x^4+7x^3+12x^2)+(x^2+x^2)+(3x+4x)+1
=(x^2+3x)(x^2+4x)+(x^2+3x)+(x^2+4x+1)
=(x^2+3x)(x^2+4x+1)+(x^2+4x+1)
=(x^2+3x+1)(x^2+4x+1)