Video: Factorising the Difference of Two Cubes

Completely factor 64π‘₯Β³ βˆ’ 125𝑦³.


Video Transcript

Completely factor 64π‘₯ cubed minus 125𝑦 cubed.

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

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

So here we can see we’ve plugged in four π‘₯ for π‘Ž and five 𝑦 for 𝑏. But we need to simplify. Four π‘₯ squared is equal to 16π‘₯ squared, and four π‘₯ times five 𝑦 is equal to 20π‘₯𝑦. And five 𝑦 squared is equal to 25𝑦 squared. Therefore, after factoring completely, we get an answer of four π‘₯ minus five 𝑦 times 16π‘₯ squared plus 20π‘₯𝑦 plus 25𝑦 squared.

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