For Problems , use the sum-of-two-cubes or the difference-of-two-cubes pattern to factor each of the following. (Objective 2)
The given problem by the use of the sum-of-cubes pattern or the difference-of-cubes pattern.
i) Polynomial in the form of The Sum of Two Squares pattern like is not factorable using integers.
ii) The Sum of Two Cubes pattern is .
iii) The Difference of Two Squares pattern is .
iv) Multiplication is commutative, so the order of writing the factors is not important. For example, can also be written as .
The following steps have been followed to find out the factors:
Step-1: Convert the polynomial in the form of 2 cubes with addition or subtraction and compare with the sum of two cubes pattern or the difference of two cubes pattern.
Step-2: Replace the value of and in the sum of two cubes pattern or in the difference of two cubes pattern by the binomial values available from the step-2 and simplify.
The given polynomial is .
It can be written as,
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