Разложите ** множители 1)2u^3-2v^3 2)3z^3+3w^3 3)nx^3+nz^3 4)w^4-w 5)z^4+8z 6)x^4-16z^4...

Question

Разложите на множители
1)2u^3-2v^3
2)3z^3+3w^3
3)nx^3+nz^3
4)w^4-w
5)z^4+8z
6)x^4-16z^4
7)81-k^4

Answer 1

1) 2u^3-2v^3=2(u^3-v^3)=2(u-v)(u^2+uv+v^2)

2) 3z^3+3w^3=3(z^3+w^3)=3(z+w)(z^2-zw+w^2)

3) nx^3+nz^3=n(x^3+z^3)=n(x+z)(x^2-xz+z^2)

4) w^4-w=w(w^3-1)=w(w-1)(w^2+w+1)

5) z^4+8z=z(z^3+8)=z(z+2)(z^2-2z+4)

6) x^4-16z^4=(x^2-4z^2)(x^2+4z^2)=(x-2z)(x+2z)(x^2+4z^2)

7) 81-k^4=(9-k^2)(9+k^2)=(3-k)(3+k)(9+k^2)