Q. 228 - Intermediate Algebra

Question

In the following exercises, factor completely.  

${\left(y-3\right)}^3-64y^3$

Step-by-Step Solution

Answer

The simplified expression is  $-(7y+3)(73y^2-30y+9)$

Step 1. Given Information

The given expression is ${\left(y-3\right)}^3-64y^3$

Step 2. Calculation

We will find the factor of binomial sum by using difference of cube pattern,

$$\begin{gathered} {(y-3)}^3-64y^3={(y-3)}^3-{\left(8y\right)}^3 \\ =\left(\right(y-3)-8y)({(y-3)}^2+(y-3)8y+{\left(8y\right)}^2) \\ =(y-3-8y)({(y-3)}^2+(8y^2-24y)+64y^2) \\ =(-7y-3)\left(\right(y^2-2\times y\times 3+9)+(8y^2-24y)+64y^2) \\ =(-7y-3)(73y^2-6y-24y+9) \\ =-(7y+3)(73y^2-30y+9) \end{gathered}$$