Simplifying the Expression: (5x^3+5x^2+5)(6x^36x^2+8x5)
This article will guide you through simplifying the expression: (5x^3+5x^2+5)(6x^36x^2+8x5). We will break down the steps involved in simplifying this expression.
Understanding the Expression
First, let's understand the expression. We have two polynomials separated by a subtraction sign. This indicates that we need to subtract the second polynomial from the first one.
Distributing the Negative Sign
The most important step is to distribute the negative sign across the second polynomial. This means that we multiply each term within the second polynomial by 1.

(5x^3+5x^2+5)(6x^36x^2+8x5) becomes:

(5x^3+5x^2+5) + (1)(6x^36x^2+8x5)

5x^3+5x^2+5 6x^3 +6x^2 8x + 5
Combining Like Terms
Now, we need to combine like terms. Like terms are terms with the same variable and exponent.
 5x^3  6x^3 = x^3
 5x^2 + 6x^2 = 11x^2
 8x remains the same
 5 + 5 = 10
Simplified Expression
Finally, we can combine all the simplified terms to get the simplified expression:
x^3 + 11x^2  8x + 10
Therefore, the simplified form of the expression (5x^3+5x^2+5)(6x^36x^2+8x5) is x^3 + 11x^2  8x + 10.