Question

Запишите выражение в виде произведение a^3+b^6, x^9-y^3, x^6+y^6, x^6+y^3, p^3-q^9 ,m^9-n^9

Answer 1

$a^3+b^6=(a+b^2)(a^2-ab^2+b^4)\\\\x^9-y^3=(x^3-y)(x^6+x^3y+y^2)\\\\x^6+y^6=(x^2+y^2)(x^4-x^2y^2+y^4)\\\\x^6+y^3=(x^2+y)(x^4-x^2y+y^2)\\\\p^3-q^9=(p-q^3)(p^2+pq^3+q^6)\\\\\\m^9-n^9=(m^3-n^3)(m^6+m^3n^3+n^6)=\\\\=(m-n)(m^2+mn+n^2)(m^6+m^3n^3+n^6)$

Answer 2

Выражения в виде произведений:

1. a^3 + b^6 = (a^3)(1) + (b^2)^3 = (a^3)(1) + (b^2)^2(b^4) = a^3 + b^2(b^4)

2. x^9 - y^3 = (x^3)^3 - (y^1)^3 = (x^3 - y)(x^6 + x^3y + y^2)

3. x^6 + y^6 = (x^3)^2 + (y^3)^2 = (x^3 + y^3)(x^3 - y^3)

4. x^6 + y^3 = (x^2)^3 + (y^1)^3 = (x^2 + y)(x^4 - x^2y + y^2)

5. p^3 - q^9 = (p^1)^3 - (q^3)^3 = (p - q^3)(p^2 + pq^3 + q^6)

6. m^9 - n^9 = (m^3)^3 - (n^3)^3 = (m^3 - n^3)(m^6 + m^3n^3 + n^6)