Completely factor 64𝑥 cubed minus 125𝑦 cubed.
Here we have an expression called a difference of cubes. So we have 𝑎 cubed minus 𝑏 cubed. And the formula for that is 𝑎 minus 𝑏 times 𝑎 squared plus 𝑎𝑏 plus 𝑏 squared. So 𝑎 cubed must be equal to 64𝑥 cubed, and 𝑏 cubed must be equal to 125𝑦 cubed. So we need to solve for 𝑎 and 𝑏. That way, we can use it in our formula. So we said 𝑎 cubed equal to 64𝑥 cubed, and we said 𝑏 cubed equal to 125𝑦 cubed.
In order to solve for 𝑎, we need to cube-root both sides of the equation. And we find that 𝑎 is equal to four 𝑥. 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 𝑎 and plug in 𝑏.
So here we can see we’ve plugged in four 𝑥 for 𝑎 and five 𝑦 for 𝑏. But we need to simplify. Four 𝑥 squared is equal to 16𝑥 squared, and four 𝑥 times five 𝑦 is equal to 20𝑥𝑦. And five 𝑦 squared is equal to 25𝑦 squared. Therefore, after factoring completely, we get an answer of four 𝑥 minus five 𝑦 times 16𝑥 squared plus 20𝑥𝑦 plus 25𝑦 squared.