Question

Please Please Please Help Me

Write the expressions as a product:

x^3–y^6

a^6+b^3

m^9–n^3

p^3+k^9

a^6+b^9

x^9–y^9

Answer 1

1. (x-y^2)(x^2 +xy^2 +y^4)
2. (a^2 +b)(a^4 -a^2b +b^2)
3. (m^3-n)(m^6 +m^3n +n^2)
4. (p+k^3)(p^2 -pk^3 +k^6)
5. (a^2+b^3)(a^4 -a^2b^3 +b^6)
6. (x-y)(x^2 +xy +y^2)(x^6 +x^3y^3 +y^6)

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.