Simplifying Polynomial Expressions: (8a^23a+4)(5a^22a16)
This article will guide you through simplifying the polynomial expression: (8a^23a+4)(5a^22a16).
Understanding the Basics
Before we begin, let's understand some fundamental concepts:
 Polynomial: An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
 Like Terms: Terms with the same variable and exponent. For example, 3a^2 and 5a^2 are like terms, while 3a^2 and 3a are not.
 Simplifying: Combining like terms to express the polynomial in its most compact form.
StepbyStep Solution

Distribute the Negative Sign: The minus sign before the second parenthesis indicates we need to multiply each term inside by 1.
(8a^2  3a + 4) + (5a^2 + 2a + 16)

Combine Like Terms: Group together terms with the same variable and exponent:
(8a^2 + 5a^2) + (3a + 2a) + (4 + 16)

Simplify: Combine the coefficients of each group of like terms:
13a^2  a + 20
Final Result
The simplified expression is 13a^2  a + 20.