Question

122
course
ap precalculus
due wed, oct 22, 2025
55
default gallery

1. 27y³ - 8

text math set matrix
answer

Explanation:

Step1: Recognize the difference of cubes formula

The formula for the difference of cubes is \(a^{3}-b^{3}=(a - b)(a^{2}+ab + b^{2})\). In the expression \(27y^{3}-8\), we can rewrite \(27y^{3}=(3y)^{3}\) and \(8 = 2^{3}\). Here \(a = 3y\) and \(b=2\).

Step2: Apply the difference of cubes formula

Substitute \(a = 3y\) and \(b = 2\) into the formula \(a^{3}-b^{3}=(a - b)(a^{2}+ab + b^{2})\).
We get \((3y)^{3}-2^{3}=(3y - 2)[(3y)^{2}+(3y)\times2+2^{2}]\).

Step3: Simplify the expanded form

Calculate \((3y)^{2}=9y^{2}\), \((3y)\times2 = 6y\), and \(2^{2}=4\).
So the factored form is \((3y - 2)(9y^{2}+6y + 4)\).

Answer:

\((3y - 2)(9y^{2}+6y + 4)\)