91Ó°ÊÓ

When dealing with binomials, a powerful tool we use is the binomial expansion. A binomial is an algebraic expression containing two terms, such as \( (a + b) \) or \( (a - b) \). To expand a binomial squared, we use the binomial formula. For the given problem, the expression is \( (\text{√}x - 3)^{2} \). Using the binomial formula for squaring, \( (a - b)^{2} = a^{2} - 2ab + b^{2}\), we identify \( a = \text{√}x \) and \( b = 3 \). Substituting these values into the formula, we can start expanding the expression step by step. Binomial expansion helps us break down and understand the individual parts of the expression more clearly.

Simplifying expressions is a crucial step in solving algebraic problems. Each term within the expanded binomial must be simplified individually. Starting with \( (\text{√}x)^{2} \), this simplifies cleanly to \( x \) because \( (\text{√}x)^{2} = x \). The next term \( -2 \text{√}x \cdot 3 \) simplifies to \( -6 \text{√}x \). Finally, \( 3^{2} \) simplifies to \( 9 \). Combining these simplified terms provides us with \( x - 6 \text{√}x + 9 \). Breaking down and simplifying each term individually can make the process feel more manageable and ensures accuracy.

Performing algebraic operations correctly is essential in algebra. We frequently use operations such as addition, subtraction, multiplication, and exponentiation. For the expression \( (\text{√}x - 3)^{2} \), we planned the steps ahead using the binomial formula, applied multiplication to expand it, and then used simplification to tidy up the terms. Combining \( x \), \( -6 \text{√}x \), and \( 9 \) into a single simplified expression requires careful handling of each algebraic operation. Knowing the rules of operations and the order of operations — often remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) — assures that expressions are solved methodically and correctly.