The formula in finding the sum or difference of two cubes is:
[tex]a^{3} + b^{2} = (a + b)(a^{2} - ab + b^{2} )[/tex]
[tex]a^{3} - b^{3} = (a - b)( a^{2} + ab + b^{2} )[/tex]
*Always remember that SDOTC always work with binomials.
Example:
[tex] 8 x^{6} + y^{3} [/tex]
First, we need to find the cube root of the terms of the binomial.
[tex]8x^{3} = 2 x^{2} [/tex]
[tex]y^{3} = y[/tex]
[tex]2x^{2} + y[/tex]
Next, we need to get the trinomial of the binomial on its special form.
Recall SOPAS
S - Square of the first term
O - Opposite sign of the second term
P - Product of the first and second term
A - Addition or the positive sign
S - Square of the last term or the second term
[tex](2 x^{2} + y)(4 x^{4} - 2 x^{2}y + y^{2} )[/tex]
