Question

Simplify the polynomial by combining like terms.
4.78x^2-3.55x+7.85x^2+10.35-4.06x

Answer 1

The simplified polynomial is
`y = 12.63\cdot x^(2)-7.61\cdot x + 10.35`.

Step-by-step 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)
`y = 4.78\cdot x^(2)-3.55\cdot x +7.85\cdot x^(2)+10.35 - 4.06\cdot x` Given.

2)
`y = (4.78\cdot x^(2)+7.85\cdot x^(2)) +(-3.55\cdot x-4.06\cdot x) + 10.35` Associative and commutative properties.

3)
`y = (4.78+7.85)\cdot x^(2) + (-3.55-4.06)\cdot x + 10.35` Distributive property.

4)
`y = 12.63\cdot x^(2)-7.61\cdot x + 10.35` Definitions of addition and subtraction/Result.

The simplified polynomial is
`y = 12.63\cdot x^(2)-7.61\cdot x + 10.35`.