Find the product. Simplify your answer. (2v - 1)(2v + 1) ______

Identify Special Case: Identify the special case that applies here. (2v - 1)(2v + 1) is in the form of (a - b)(a + b). Special case: (a - b)(a + b) = a^2 - b^2Identify Values of a and b: Identify the values of a and b. Compare (2v - 1)(2v + 1) with (a - b)(a + b). a = 2v b = 1Apply Difference of Squares: Apply the difference of squares to expand (2v - 1)(2v + 1). (a - b)(a + b) = a^2 - b^2 (2v - 1)(2v + 1) = (2v)^2 - 1^2Simplify Expression: Simplify (2v)^2 - 1^2. (2v)^2 - 1^2 = (2v * 2v) - (1 * 1) = 4v^2 - 1

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Find the product. Simplify your answer. $\newline$ $(2v - 1)(2v + 1)$

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Find the product. Simplify your answer.

\newline

(2v - 1)(2v + 1)

Identify Special Case: Identify the special case that applies here. $\newline$ $(2v - 1)(2v + 1)$ is in the form of $(a - b)(a + b)$ . $\newline$ Special case: $(a - b)(a + b) = a^2 - b^2$
Identify Values of $a$ and $b$ : Identify the values of $a$ and $b$ . Compare $(2v - 1)(2v + 1)$ with $(a - b)(a + b)$ . $a = 2v$ $b = 1$
Apply Difference of Squares: Apply the difference of squares to expand $(2v - 1)(2v + 1)$ . $\newline$ $(a - b)(a + b) = a^2 - b^2$ $\newline$ $(2v - 1)(2v + 1) = (2v)^2 - 1^2$
Simplify Expression: Simplify $(2v)^2 - 1^2.$ $(2v)^2 - 1^2 = (2v \times 2v) - (1 \times 1)$ $= 4v^2 - 1$