Answer:
- (x-y^2)(x^2 +xy^2 +y^4)
- (a^2 +b)(a^4 -a^2b +b^2)
- (m^3-n)(m^6 +m^3n +n^2)
- (p+k^3)(p^2 -pk^3 +k^6)
- (a^2+b^3)(a^4 -a^2b^3 +b^6)
- (x-y)(x^2 +xy +y^2)(x^6 +x^3y^3 +y^6)
Step-by-step explanation:
In every case, the factorization makes use of the standard form for factoring the sum or difference of cubes:
- a^3 +b^3 = (a +b)(a^2 -ab +b^2)
- a^3 -b^3 = (a -b)(a^2 +ab +b^2)
1. a=x, b=y^2. Use the formula for the difference.
2. a^2 ⇒ a, b = b. Use the formula for the sum.
3. a=m^3, b=n. Use the formula for the difference.
4. a=p b=k^3. Use the formula for the sum.
5. a^2 ⇒ a, b^3 ⇒ b. Use the formula for the sum.
6. a=x^3, b=y^3. Use the formula for the difference. When you do, the first factor is the difference x^3 -y^3, which can be factored using the difference formula again with a=x, b=y.
