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Find the binomial that completes the factorization.\newliney3−64=(‾)(y2+4y+16)y^3 - 64 = (\underline{\hspace{3cm}})(y^2 + 4y + 16)

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Full solution

Q. Find the binomial that completes the factorization.\newliney3−64=(‾)(y2+4y+16)y^3 - 64 = (\underline{\hspace{3cm}})(y^2 + 4y + 16)
  1. Recognize difference of cubes: Recognize that y3−64y^3 - 64 is a difference of cubes since 6464 is 434^3.
  2. Apply formula for factoring: Use the formula for factoring a difference of cubes: a3−b3=(a−b)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2).
  3. Identify values for aa and bb: Identify a=ya = y and b=4b = 4 to apply the formula.
  4. Plug values into formula: Plug aa and bb into the formula: y3−64=(y−4)(y2+4y+16)y^3 - 64 = (y - 4)(y^2 + 4y + 16).

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