# Video: Factorising the Difference of Two Cubes

Completely factor 64π₯Β³ β 125π¦Β³.

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### Video Transcript

Completely factor 64π₯ cubed minus 125π¦ cubed.

Here we have an expression called a difference of cubes. So we have π cubed minus π cubed. And the formula for that is π minus π times π squared plus ππ plus π squared. So π cubed must be equal to 64π₯ cubed, and π cubed must be equal to 125π¦ cubed. So we need to solve for π and π. That way, we can use it in our formula. So we said π cubed equal to 64π₯ cubed, and we said π cubed equal to 125π¦ cubed.

In order to solve for π, we need to cube-root both sides of the equation. And we find that π is equal to four π₯. And to solve for π, we need to do the same thing: cube-root both sides of the equation. And we find that π is equal to five π¦. So we now need to take our formula and plug in π and plug in π.

So here we can see weβve plugged in four π₯ for π and five π¦ for π. But we need to simplify. Four π₯ squared is equal to 16π₯ squared, and four π₯ times five π¦ is equal to 20π₯π¦. And five π¦ squared is equal to 25π¦ squared. Therefore, after factoring completely, we get an answer of four π₯ minus five π¦ times 16π₯ squared plus 20π₯π¦ plus 25π¦ squared.