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In algebra, 'combining like terms' is a critical step in simplifying expressions. Like terms are terms that contain the same variable raised to the same power. For example, in the expression 6y^2 + 11y^2 - 8y^2, all three terms are like terms because they all include the variable part \(y^2\).
When combining like terms, you focus exclusively on their coefficients (the numerical parts). If you have terms like 6y^2, 11y^2, and -8y^2, you just sum or subtract their coefficients: 6 + 11 - 8.
This results in 9. Finally, you attach the common variable part back to the combined coefficient, yielding a simplified expression: 9y^2.

Coefficients are the numerical parts of terms that are multiplied by the variables in an expression. In the expression 6y^2 + 11y^2 - 8y^2, the coefficients are 6, 11, and -8 respectively.
When working with algebraic expressions, coefficients are essential because they determine the numerical value of the terms.
To simplify the expression, we add and subtract these coefficients. Essentially, you're performing basic arithmetic on the numbers, which is why understanding coefficients can make algebra much more manageable.
Summing the coefficients of 6y^2 + 11y^2 - 8y^2 gives us:
6 + 11 - 8 = 9.
Therefore, the simplified coefficient of the variable part (y^2) is 9.

A polynomial is an algebraic expression made up of terms that consist of variables and coefficients. The terms are separated by addition (+) or subtraction (-). Essentially, it is a sum or difference of terms containing variables raised to whole-number exponents.
In our original problem, 6y^2 + 11y^2 - 8y^2 is a simple polynomial.
Polynomials can have multiple terms (also called 'monomials'). In our example, we have three monomials: 6y^2, 11y^2, and -8y^2.
To simplify polynomials, you often combine like terms and operate on the coefficients. This reduces the polynomial to its simplest form. For instance, our simplified polynomial becomes 9y^2 after combining like terms and working with the coefficients.