(1)x^4-7x^2y^2+9y^4(2)y^3+17y^2-3y-51(3)x^2(y-z)-4(y-z)-3x(z-y)(4)7(a-3)^2+3(a-3)-4

Question

(1)x^4-7x^2y^2+9y^4
(2)y^3+17y^2-3y-51
(3)x^2(y-z)-4(y-z)-3x(z-y)
(4)7(a-3)^2+3(a-3)-4

Answer 1

1.原式=x^4-7x^2y^2+10y^4-y^4
=(x^2-2y^2)(x^2-5y^2)-y^4
=[x^2-2y^2)+y^2][(x^2-5y^2)-y^2]
=(x^2-2y^2+y^2)(x^2-5y^2-y^2)
2.原式=(y^3+17y^2)-(3y+51)
=y^2(y+17)-3(y+17)
=(y^2-3)(y+17)
3.原式=x^2(y-z)-4(y-z)-3x(z-y)
=x^2(y-z)-4(y-z)+3x(y-z)
=(x^2+3x-4)(y-z)
=(x+4)(x-1)(y-z)
4.原式=7(a-3)^2+3(a-3)-4
=[(a-3)+1][7(a-3)-4]
=(a-2)(7a-21-4)
=(a-2)(7a-25)