In Exercises 15–58, find each product. (4x2−1)2

Ch. P - Fundamental Concepts of Algebra

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Ch. P - Fundamental Concepts of Algebra

Problema 47

Capitolo 1, Problema 47

In Exercises 15–58, find each product. (4x²−1)²

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Recognize that the expression $(4x^2 - 1)^2$ is a binomial squared. Use the formula for the square of a binomial: $(a - b)^2 = a^2 - 2ab + b^2$.

Identify $a = 4x^2$ and $b = 1$ in the given expression.

Apply the formula: $(4x^2 - 1)^2 = (4x^2)^2 - 2(4x^2)(1) + (1)^2$.

Simplify each term: $(4x^2)^2 = 16x^4$, $-2(4x^2)(1) = -8x^2$, and $(1)^2 = 1$.

Combine the simplified terms to express the expanded form: $16x^4 - 8x^2 + 1$.

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