and \( x y=21 \) find \( x^{3}+y^{3} \) \( x^{3}+y^{3}=(x+y) \)

It seems you're looking to find \( x^{3} + y^{3} \) given that \( xy = 21 \). To determine \( x^{3} + y^{3} \), additional information about the sum \( x + y \) is typically required. However, I can provide you with a general formula that relates these expressions. ### Formula for \( x^{3} + y^{3} \) The sum of cubes can be expressed in terms of \( x + y \) and \( xy \) using the following identity: \[ x^{3} + y^{3} = (x + y)^3 - 3xy(x + y) \] ### Applying the Given Information Given: \[ xy = 21 \] Plugging this into the formula: \[ x^{3} + y^{3} = (x + y)^3 - 3 \times 21 \times (x + y) \] \[ x^{3} + y^{3} = (x + y)^3 - 63(x + y) \] ### What You Need Next To find a numerical value for \( x^{3} + y^{3} \), you need to know the value of \( x + y \). If you have that information, you can substitute it into the equation above to compute \( x^{3} + y^{3} \). ### Example **Suppose** \( x + y = 6 \): \[ x^{3} + y^{3} = 6^3 - 63 \times 6 = 216 - 378 = -162 \] **However**, if you don't have \( x + y \), you can only express \( x^{3} + y^{3} \) in terms of \( x + y \) as shown above. --- **Summary:** Given \( xy = 21 \), the expression for \( x^{3} + y^{3} \) in terms of \( x + y \) is: \[ x^{3} + y^{3} = (x + y)^3 - 63(x + y) \] If you can provide or determine \( x + y \), you can then calculate a specific value for \( x^{3} + y^{3} \).