Question

因式分解x的4次方减46X^加25

Answer 1

1.x^4-46x^2+25

=x^4-10x^2+25-36x^2

=(x^2-5)^2-(6x)^2

=(x^2-6x-5)(x^2+6x-5);

2.(XY+1)(X+1)(Y+1)+XY

=(xy+1)(xy+1+x+y)+xy

=x^2y^2+xy+x^2y+xy^2+xy+1+x+y+xy

=x^2y^2+x^2y+xy^2+3xy+x+y+1

=(x^2y^2+2xy+1)+x^2y+xy^2+xy+x+y

=(xy+1)^2+xy(x+y)+(x+y)+xy

=(xy+1)^2+(x+y)(xy+1)+xy