Respuesta :
Like term's coefficient are added in addition of algebraic terms. The simplified form of the given expression is [tex]x^3 + 8x^2 + 13[/tex]
What are like terms?
Those terms which have same variables raised with same power.
For example, [tex]5t^3[/tex] and [tex]6t^3[/tex] are like terms since variable is same, and it is raised to same power 3.
For example [tex]x^3[/tex] and [tex]3x^4[/tex] are not like terms as the variables are same but powers aren't same.
What are coefficients?
Constants who are in multiplication with variables are called coefficients of those variables.
When can we add or subtract terms of polynomial by their coefficient's addition or subtraction?
Suppose we have
[tex]5x^2 + 6y[/tex]
Since those terms are not like terms, their coefficient won't be add and the expression we've got right now, is its simplest form and cannot be reduced more.
If we have, suppose,
[tex]4x + 5x^2 + 2x[/tex]
then we see that [tex]4x[/tex] and [tex]2x[/tex] are like terms, their coefficient can be added and thus, the simplified form would be
[tex](4+2)x + 5x^2 = 6x + 5x^2[/tex]
For the given case, the considered expression is simplified as:
[tex]= > (6x^2 - 3 + 5x^3) - (4x^3 - 2x^2 - 16)\\= 6x^2 - 3 + 5x^3 -4x^3 + 2x^2 + 16\\ = 5x^3 - 4x^3 + 6x^2 + 2x^2 - 3 + 16\\= (5-4)x^3 + (6+2)x^2 + 13\\= 1.x^3 + 8x^2 + 13 \\= x^3 + 8x^2 + 13[/tex]
(variables with 1 as coefficient is not written explicitly as 1 is factor of all measurements).
Sign multiply by
[tex]-ve \times (+ve) = -ve\\(-ve) \times (-ve) = +ve\\(+ve) \times (+ve) = +ve\\(+ve) \times (-ve) = -ve[/tex]
where -ve, +ve are sign of operands and result.
Thus, the simplified form of the given expression is [tex]x^3 + 8x^2 + 13[/tex]
Learn more about simplification of expressions here:
https://brainly.com/question/26437497
