slot 13 - Flexi answers - How can I find the cubes of numbers using a shortcut method? | CK-12 Foundation slot mega 888

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To find the cubes of numbers using a shortcut method, you can use the concept of patterns and algebraic formulas. Here's a simple shortcut method for finding the cubes of numbers: Shortcut Method for Cubing Numbers: Identify the cube of a nearby smaller number that you already know. Express the number you want to cube as the sum of the nearby smaller number and the difference between the two numbers. Use the algebraic formula for the cube of a binomial @$\begin{align*}(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\end{align*}@$ to find the cube of the number. Let's take an example to illustrate this: Example: Find the cube of 13 using the shortcut method. Identify the cube of a nearby smaller number: The cube of 10 is 1000 (@$\begin{align*}10^3\end{align*}@$ ). Express 13 as the sum of 10 and the difference between 13 and 10: 13 = 10 + (13 - 10). Apply the formula: @$\begin{align*}&{(a + b)}^3 = a^3 + 3a^2b + 3ab^2 + b^3:\\ &(10 + (13 - 10))^3 = 10^3 + 3 * 10^2 * (13 - 10) + 3 * 10 * (13 - 10)^2 + (13 - 10)^3\\ &(10 + 3)^3 = 1000 + 3 * 100 * 3 + 3 * 10 * 9 + 3^3\\ &13^3 = 1000 + 900 + 270 + 27\\ &13^3 = 2197\end{align*}@$   So, the cube of 13 is 2197. This method can be used for other numbers as well, and with practice, you'll become more efficient at finding the cubes of numbers using this shortcut.

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