Here are the essential concepts you must grasp in order to answer the question correctly.
Binomial Expansion
Binomial expansion refers to the process of expanding expressions that are raised to a power, particularly those in the form of (a + b)^n. The expansion can be achieved using the Binomial Theorem, which states that (a + b)^n = Σ (n choose k) * a^(n-k) * b^k, where k ranges from 0 to n. This concept is essential for simplifying expressions like (a - 6b)^2.
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Square of a Binomial
The square of a binomial, expressed as (x + y)^2, can be simplified using the formula x^2 + 2xy + y^2. For the expression (a - 6b)^2, this means applying the formula to find a^2, subtracting 2 times a times 6b, and adding (6b)^2. Understanding this formula is crucial for accurately calculating the product.
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Algebraic Simplification
Algebraic simplification involves reducing expressions to their simplest form by combining like terms and applying arithmetic operations. In the context of the expression (a - 6b)^2, after expanding, one must combine the resulting terms to achieve a final simplified expression. Mastery of this concept is vital for effectively solving algebraic problems.
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