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Visual proof of the formulas for the sum and difference of two cubes. In mathematics, the sum of two cubes is a cubed number added to another cubed number.
Below are identities whose left-hand sides are commonly used as patterns (this means that the variables E and F that appear in these identities may represent any subexpression of the expression that has to be factorized). [6] Visual proof of the differences between two squares and two cubes. Difference of two squares
The difference of two squares can also be used as an arithmetical short cut. If two numbers (whose average is a number which is easily squared) are multiplied, the difference of two squares can be used to give you the product of the original two numbers. For example: = (+)
With even cubes, there is considerable restriction, for only 00, o 2, e 4, o 6 and e 8 can be the last two digits of a perfect cube (where o stands for any odd digit and e for any even digit). Some cube numbers are also square numbers; for example, 64 is a square number (8 × 8) and a cube number (4 × 4 × 4).
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Like pattern blocks, interlocking cubes can also be used for teaching patterns. Students may use the cubes to make long trains of patterns. Like the pattern blocks, the interlocking cubes provide a concrete experience for students to identify, extend, and create patterns. The difference is that a student can also physically decompose a pattern ...
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The sum of the n first cubes is the square of the sum of ... The difference between any two odd perfect squares is a multiple of 8. ... An analogous pattern applies ...