In Exercises 15–58, find each product. (9−5x)2

Ch. P - Fundamental Concepts of Algebra

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Ch. P - Fundamental Concepts of Algebra

Problema 50

Capitolo 1, Problema 50

In Exercises 15–58, find each product. (9−5x)²

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Recognize that the expression $(9 - 5x)^2$ represents a binomial squared. To expand this, use the formula for the square of a binomial: $(a - b)^2 = a^2 - 2ab + b^2$.

Identify the terms in the binomial: $a = 9$ and $b = 5x$.

Apply the formula $(a - b)^2 = a^2 - 2ab + b^2$: Substitute $a = 9$ and $b = 5x$ into the formula.

Calculate each term: $a^2 = 9^2$, $-2ab = -2(9)(5x)$, and $b^2 = (5x)^2$.

Combine the results from the previous step to write the expanded form of the expression.

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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. In this case, (9 - 5x)^2 is a binomial expression that can be expanded using this theorem.

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