Quadratic expressions are mathematical expressions that have the power of one of its alphabets being equal to and not more than two. The given expression in the question can be simplified as 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
Algebraic expressions are mathematical expressions that consist of given number(s) and alphabet(s). When the power (exponential) of one of the alphabets is given as two, then the expression can be classified as a quadratic expression.
Thus the given expansion of the quadratic expression can be simplified as follows:
([tex]9x^{2}[/tex] + 9x - 4)([tex]9x^{2}[/tex] + 9x - 10) - 72
But,
([tex]9x^{2}[/tex] + 9x - 4)([tex]9x^{2}[/tex] + 9x - 10) = [tex]9x^{2}[/tex]([tex]9x^{2}[/tex] + 9x - 10) + 9x([tex]9x^{2}[/tex] + 9x - 10) - 4([tex]9x^{2}[/tex] + 9x - 10)
= 81[tex]x^{4}[/tex] + 81[tex]x^{3}[/tex] - 90[tex]x^{2}[/tex] + 81[tex]x^{3}[/tex] + 81 [tex]x^{2}[/tex] - 90x - 36 [tex]x^{2}[/tex] + 36x - 40
= 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40
So that we have;
(81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40) - 72 = 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 40 -72
= 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
Thus the simplification of the given expression is 81[tex]x^{4}[/tex] + 162[tex]x^{3}[/tex] - 45[tex]x^{2}[/tex] - 54x - 112
For more clarifications on the simplification of algebraic expressions, visit: https://brainly.com/question/26581327
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