Question

x^5-3x^3-28因式分解因式分解x^5-3x^3-28x3a^2x-4b^3y+3b^3x-4a^3y(ax+by

Answer 1

x^5-3x^3-28x

=x(x^4-3x^2-28)

=x(x^2-7)(x^2+4)

3a^2x-4b^3y+3b^3x-4a^2y

=a^2(3x-4y)+b^3(3x-4y)

=(3x-4y)(a^2+b^3)

(ax+by)^2+(bx-ay)^2

=a^2x^2+2abxy+b^2y^2+b^2x^2-2abxy+a^2y^2

=a^2x^2+b^2y^2+b^2x^2+a^2y^2

=(a^2x^2+b^2x^2)+(b^2y^2+a^2y^2)

=x^2(a^2+b^2)+y^2(b^2+a^2)

=(a^2+b^2)(x^2+y^2)