Factor difference and sums of cubes. Explain sums and differences of cubes as polynomial identities.
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The diagram below shows a cube of dimensions $$B$$ subtracted from a cube of dimensions $$A$$. The total volume represents $$ A^3-B^3$$.
The diagram below shows the volume of $$ A^3-B^3$$ subdivided into smaller volumes. Find the formula for the difference of two cubes using the smaller volumes shown.
Difference of Cubes by Alex Toole is made available by YouTube under the Standard YouTube License. Accessed Sept. 26, 2017, 3:13 p.m..
Determine if the following are factors of the cubic polynomials shown:
Is $${(a-b)}$$ a factor of $${a^3-b^3}$$?
Is $${(a+b)}$$ a factor of $${a^3+b^3}$$?
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Factor the following expressions and verify that the factored expression is equivalent to the original.
$${16x^6+2y^3}$$
$${16x^6-2y^3}$$
How are the two factored expressions different?