Answer:
The expression is equivalent to [tex]-4\cdot x^{2}+3\cdot x -5[/tex].
Step-by-step explanation:
In this exercise we must transform [tex]-4\cdot x^{2}+2\cdot x -5\cdot (1+x)[/tex] into its standard form, that is a polynomial of the form:
[tex]y = a\cdot x^{2} + b\cdot x + c[/tex] (1)
Where:
[tex]y[/tex] - Dependent variable.
[tex]x[/tex] - Independent variable.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients.
Let [tex]y = -4\cdot x^{2}+2\cdot x -5\cdot (1+x)[/tex], now we proceed to convert it into its standard form:
1) [tex]-4\cdot x^{2}+2\cdot x -5\cdot (1+x)[/tex] Given
2) [tex](-4)\cdot x^{2}+2\cdot x + (-5)\cdot (1+x)[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]
3) [tex](-4)\cdot x^{2}+2\cdot x +(-5)\cdot 1 +(-5)\cdot x[/tex] Distributive property
4) [tex](-4)\cdot x^{2}+[5+(-2)]\cdot x -5[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]/Commutative and distributive properties
5) [tex]-4\cdot x^{2}+3\cdot x -5[/tex] [tex](-a)\cdot b = -a\cdot b[/tex]/Definition of subtraction/Result
The expression is equivalent to [tex]-4\cdot x^{2}+3\cdot x -5[/tex].
