Question

State the conjugate of each binomial. $$-b+2$$

Short answer

Answer: The conjugate of the binomial -b+2 is -b-2.

Step-by-step solution

Identify the binomial

The given binomial is \(-b+2\).

Find the conjugate

To find the conjugate, we will change the sign between the terms. So, the conjugate of \(-b+2\) is \(-b-2\). The conjugate of the binomial \(-b+2\) is \(\boldsymbol{-b-2}\).

Key concepts

Binomials

A binomial is an algebraic expression composed of two terms connected by a plus or minus sign. In our example,

• \(-b+2\) is a binomial with two terms: \(-b\) and \(2\).
• The sign between these terms is a plus, which indicates how they are related.

Binomials play a critical role in algebra because they serve as building blocks for more complex expressions. They are frequently used in operations like addition, subtraction, multiplication, and especially in forming conjugates.

Algebraic Expressions

Algebraic expressions are combinations of variables, numbers, and arithmetic operations. These expressions help us to represent mathematical ideas in a symbolic form. For instance:

• The expression \(-b + 2\) consists of a variable \(b\) and a constant \(2\).
• Each part of the expression can be manipulated with algebraic rules.

Expressions allow us to work with unknown values and form equations. Simplifying or rearranging these expressions is a fundamental skill in algebra, leading us to solve equations or make predictions.

Prealgebra Concepts

Prealgebra sets the stage for understanding algebraic expressions and equations. It covers fundamental ideas such as identifying parts of an expression and basic operations. Topics like the concept of conjugates become essential, as seen in:

• Identifying a conjugate involves changing the sign between the terms of a binomial. For example, \(-b + 2\) has a conjugate \(-b - 2\).
• Understanding these basic manipulations provides a solid foundation for more advanced algebra.
• Prealgebra emphasizes key concepts like variables and constants, forming the basis for future mathematical studies.

These foundational skills are crucial for anyone starting their journey into algebra.