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In algebra, the concept of like terms is fundamental to simplifying expressions. Like terms are terms that have the same variables raised to the same powers. Essentially, they look similar except for their coefficients, which are the numbers multiplying the variables. When simplifying polynomial expressions, recognizing like terms allows you to combine these terms to simplify the expression further. For instance, in the expression \(9d^2 + 6d + 8d - 4d^2\), \(9d^2\) and \(-4d^2\) are like terms because they both contain the same variable \(d^2\). Likewise, \(6d\) and \(8d\) are like terms because they both contain the variable \(d\) raised to the same power. Steps To Identify Like Terms:

• Look for the same variable.
• Check for the exact same power or exponent for each variable.
• Ensure coefficients are the only difference between terms.

Mastering the identification of like terms is crucial in performing algebraic operations effectively.

Simplifying an algebraic expression means reducing it to its simplest form. This entails combining like terms, eliminating any unnecessary parts, and obtaining the most straightforward version possible. Simplifying expressions allows us to work with them more easily and predict the effects of changes more clearly.In our exercise, the expression \((9d^2 + 6d) + (8d - 4d^2)\) is simplified by first identifying and then combining like terms. Steps to Simplify an Expression:

• Identify all like terms within the expression.
• Rearrange the expression to group like terms together.
• Combine the like terms by adding or subtracting their coefficients.

Following these steps reduces the expression to \(5d^2 + 14d\), allowing you to work with a much cleaner and more manageable polynomial.

Algebraic operations form the backbone of algebra, facilitating manipulation of expressions and equations. They include addition, subtraction, multiplication, division, and so on, applied within the framework of algebraic rules.In polynomial addition, like in the given exercise \((9d^2 + 6d) + (8d - 4d^2)\), it’s all about combining terms effectively. The operation begins with the identification of like terms, followed by rearranging and combining them through addition or subtraction.Key Points About Algebraic Operations In Polynomials:

• Algebraic operations follow specific rules, like the distributive and associative properties.
• Operations on polynomials typically involve handling coefficients separately from variables.
• When adding polynomials, focus on aligning like terms to ensure correct results.

Understanding and mastering algebraic operations can significantly enhance your ability to tackle complex algebraic expressions effortlessly.