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 theorem provides a systematic way to calculate the coefficients of the expanded terms.
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Squaring a Binomial
Squaring a binomial involves multiplying the binomial by itself. For a binomial (a + b), the square is calculated as (a + b)(a + b), which results in a^2 + 2ab + b^2. This formula is essential for simplifying expressions like (9x + 7y)^2, as it allows for the direct computation of the resulting polynomial.
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Polynomial Terms
Polynomial terms are expressions that consist of variables raised to non-negative integer powers, multiplied by coefficients. In the context of the expression (9x + 7y)^2, the resulting polynomial will contain terms such as x^2, xy, and y^2, each representing different degrees of the variables. Understanding how to combine like terms and identify the degree of the polynomial is crucial for simplifying the final expression.
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