Question

分解因式：①x^2+3y-xy-3x②x^3+2x^2y-9x-18y③(y+2)x^2+(y+2)x-12y-24

Answer 1

①x^2+3y-xy-3x

=x(x-y)-3(x-y)

=(x-y)(x-3)

②x^3+2x^2y-9x-18y

=x²(x+2y)-9(x+2y)

=(x+2y)(x²-9)

=(x+2y)(x-3)(x+3)

③(y+2)x^2+(y+2)x-12y-24

=(y+2)x²+(y+2)x-12(y+2)

=(y+2)(x²+x-12)

=(y+2)(x+4)(x-3)

④m平方x平方+n平方y平方-n平方x平方

=x²(m²-n²)+n²y²

=x²(m-n)(m+n)+n²y²