# Perfect cube decomposition question

• Nov 28th 2009, 10:27 AM
vd853
Perfect cube decomposition question
can someone explain to me how they got \$\displaystyle (4x - y)\$ in the numerator?

problem: \$\displaystyle ( 64x^3 - y^3 ) / ( 4x^2 - 33xy + 8y^2 )\$

first step: \$\displaystyle [ ( 4x - y ) ( 16x^2 + 4xy + y^2 ) ] / [ ( 4x - y ) ( x - 8y ) ]\$

I know they used the perfect cube formula, but why use 16 and 4. and where did the \$\displaystyle (4x - y)\$ come from?
• Nov 28th 2009, 10:54 AM
masters
Quote:

Originally Posted by vd853
can someone explain to me how they got \$\displaystyle (4x - y)\$ in the numerator?

problem: \$\displaystyle ( 64x^3 - y^3 ) / ( 4x^2 - 33xy + 8y^2 )\$

first step: \$\displaystyle [ ( 4x - y ) ( 16x^2 + 4xy + y^2 ) ] / [ ( 4x - y ) ( x - 8y ) ]\$

I know they used the perfect cube formula, but why use 16 and 4. and where did the \$\displaystyle (4x - y)\$ come from?

Hi vd853,

The general factorization model for the differernce of two cubes is:

\$\displaystyle (a^3-b^3)=(a-b)(a^2+ab+b^2)\$

Your numerator could be re-written as \$\displaystyle ((4x)^3-y^3)\$

Using this and the model, we come up with \$\displaystyle (4x-y)(16x^2+4xy+y^2)\$
• Nov 28th 2009, 01:55 PM
vd853
Thanks! did not know about the difference formula.