The method of factoring a polynomial in the form of the difference of two cubes is called factorization by the difference of two Cubes
The difference between cubes of two expressions forms a polynomial in mathematics. In some cases, it should be factorized as a product of factors and it is possible to factorize the difference of two cubes mathematically by the difference of cubes factoring formula.
The factoring formula for the difference of two cubes is written algebraically in two forms as follows.
You can use any one of them as a formula to factorise the difference of two cubes expression.
Now, let’s see some examples to know how to factorize the difference of two cubes by the difference of cubes factoring formula.
Factorize $27-p^3$
The second term is in cube form. If the first term is expressed in cube form, then it can be factored by the difference of cubes factoring formula. So, let’s express the first term $27$ in cube form.
$=\,\,$ $3 \times 3 \times 3-p^3$
$=\,\,$ $3^3-p^3$
Let’s denote $a = 3$ and $b = p$.
$a^3-b^3$ $\,=\,$ $(a-b)(a^2+ab+b^2)$
Now, substitute the values of $a$ and $b$ in the factorization formula.
$\implies$ $3^3-p^3$ $\,=\,$ $(3-p)(3^2+3 \times p+p^2)$
$\,\,\,\,\therefore\,\,\,\,\,$ $3^3-p^3$ $\,=\,$ $(3-p)(9+3p+p^2)$
The above simple example problem on factoring the difference of two cubes algebraic expression teaches you the process of factoring a polynomial in the form of difference between two cubes. Now, let’s exercise the questions on factorization by the difference of two cubes by following the above procedure.
The questions on factoring the difference of two cubes polynomials for your practice and solutions with understandable simple steps.
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