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Find the binomial that completes the factorization. \newlineq3+r3=(‾)(q2−qr+r2)q^3 + r^3 = (\underline{\hspace{3cm}})(q^2 - qr + r^2)

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Full solution

Q. Find the binomial that completes the factorization. \newlineq3+r3=(‾)(q2−qr+r2)q^3 + r^3 = (\underline{\hspace{3cm}})(q^2 - qr + r^2)
  1. Recognize formula: Recognize the sum of cubes formula: a3+b3=(a+b)(a2−ab+b2)a^3 + b^3 = (a + b)(a^2 - ab + b^2).
  2. Apply to q3+r3q^3 + r^3: Apply the formula to q3+r3q^3 + r^3, so the missing binomial is (q+r)(q + r).
  3. Check factorization: Check the factorization: (q+r)(q2−qr+r2)(q + r)(q^2 - qr + r^2) should equal q3+r3q^3 + r^3.

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