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In algebra, it's important to understand the concept of like terms. Like terms are terms that have the same variable raised to the same power.
For example, in the context of polynomials, the terms \(5y^2\) and \(6y^2\) are like terms because they both contain \(y^2\).
However, \(5y^2\) and \(12y\) are not like terms because one has \(y\) and the other has \(y^2\).

Identifying like terms is a key step in simplifying expressions and solving equations involving polynomials. When you add polynomials, you can only combine like terms. This concept helps ensure that you're adding correctly and simplifying your polynomials properly.

Each term in a polynomial has a number in front of the variable, called the coefficient. In the term \(5y^2\), the coefficient is 5. In \(6y^2\), the coefficient is 6.
Understanding coefficients is crucial because when you add or subtract polynomials, you are essentially adding or subtracting the coefficients of like terms.

For example, consider the problem \((5y^2 + 12y + 4) + (6y^2 - 8y + 7)\). To add these polynomials, follow these steps:

• Identify the like terms: \(5y^2\) and \(6y^2\), \(12y\) and \(-8y\), and the constants \(4\) and \(7\).
• Add the coefficients of the like terms: \(5 + 6 = 11\), \(12 - 8 = 4\), and \(4 + 7 = 11\).

This will give you the final combined polynomial \(11y^2 + 4y + 11\).

Polynomials are mathematical expressions consisting of variables and coefficients. They are made up of terms, which are separated by addition or subtraction. Each term includes a variable raised to a non-negative integer exponent, like \(y^2\), \(y\), or a constant.

Polynomials can have one term (monomials), two terms (binomials), or many terms (polynomials). In the given exercise, \(5y^2 + 12y + 4\) and \(6y^2 - 8y + 7\) are both polynomials.
Adding or subtracting polynomials involves combining like terms. This simplification process helps to write polynomials in their simplest form, making it easier to work with them in further calculations.

Using the given problem, we combined the like terms to obtain the final simplified polynomial: \(11y^2 + 4y + 11\). Understanding and mastering these core concepts will significantly improve your skills in working with polynomials.