Questions: Factor the binomial: y^3-27

Factor the binomial: y^3-27
Transcript text: Factor the binomial: $y^{3}-27$
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Solution

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Solution Steps

Step 1: Identify the Polynomial

We are given the binomial y3−27 y^{3} - 27 . This expression can be recognized as a difference of cubes, since 27 27 can be expressed as 33 3^3 .

Step 2: Apply the Difference of Cubes Formula

The difference of cubes can be factored using the formula: a3−b3=(a−b)(a2+ab+b2) a^3 - b^3 = (a - b)(a^2 + ab + b^2) In our case, let a=y a = y and b=3 b = 3 . Thus, we can rewrite the expression as: y3−33 y^{3} - 3^{3}

Step 3: Factor the Expression

Applying the difference of cubes formula, we have: y3−27=(y−3)(y2+3y+9) y^{3} - 27 = (y - 3)(y^{2} + 3y + 9)

Final Answer

The factorized form of the polynomial y3−27 y^{3} - 27 is: (y−3)(y2+3y+9) \boxed{(y - 3)(y^{2} + 3y + 9)}

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