Question

Find the value of 53^3 using the identity (x + y)3 = x3 + 3x2y + 3xy2 + y3. Show all work.

Answer 1

148877

Explanation:

We can calculate the value of 53^3, following the following identity:

`\begin{gathered} \mleft(x+y\mright)^3=x^3+3x^2y+3xy^2+y^3 \\ \text{ in this case:} \\ (50+3)^3=50^3+3\cdot50^2\cdot3+3\cdot50\cdot3^2+3^3 \\ (50+3)^3=125000+3\cdot2500\cdot3+3\cdot50\cdot9+27 \\ (50+3)^3=125000+22500+1350+27 \\ (50+3)^3=148877 \\ 53^3=148877 \end{gathered}`