Answer:
The simplified polynomial is [tex]y = 12.63\cdot x^{2}-7.61\cdot x + 10.35[/tex].
Explanation:
Combining like terms consists in apply Commutative, Associative and Distributive Properties if needed in a given algebraic expression. We proceed to present the procedure to simplify the expression by combining like terms:
1) [tex]y = 4.78\cdot x^{2}-3.55\cdot x +7.85\cdot x^{2}+10.35 - 4.06\cdot x[/tex] Given.
2) [tex]y = (4.78\cdot x^{2}+7.85\cdot x^{2}) +(-3.55\cdot x-4.06\cdot x) + 10.35[/tex] Associative and commutative properties.
3) [tex]y = (4.78+7.85)\cdot x^{2} + (-3.55-4.06)\cdot x + 10.35[/tex] Distributive property.
4) [tex]y = 12.63\cdot x^{2}-7.61\cdot x + 10.35[/tex] Definitions of addition and subtraction/Result.
The simplified polynomial is [tex]y = 12.63\cdot x^{2}-7.61\cdot x + 10.35[/tex].
