Find the product. Simplify your answer. (3p - 1)(3p + 1) ______

Identify Special Case: Identify the special case that applies to the given expression. The expression (3p - 1)(3p + 1) is in the form of (a - b)(a + b). Special case: (a - b)(a + b) = a^2 - b^2Identify Values: Identify the values of a and b. Compare (3p - 1)(3p + 1) with (a - b)(a + b). a = 3p b = 1Apply Formula: Apply the difference of squares formula to expand (3p - 1)(3p + 1). (a - b)(a + b) = a^2 - b^2 (3p - 1)(3p + 1) = (3p)^2 - (1)^2Simplify: Simplify (3p)^2 - (1)^2. (3p)^2 - (1)^2 = (3p * 3p) - (1 * 1) = 9p^2 - 1

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Find the product. Simplify your answer. $\newline$ $(3p - 1)(3p + 1)$

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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

(3p - 1)(3p + 1)

Identify Special Case: Identify the special case that applies to the given expression. $\newline$ The expression $(3p - 1)(3p + 1)$ is in the form of $(a - b)(a + b)$ . $\newline$ Special case: $(a - b)(a + b) = a^2 - b^2$
Identify Values: Identify the values of $a$ and $b$ . Compare $(3p - 1)(3p + 1)$ with $(a - b)(a + b)$ . $a = 3p$ $b = 1$
Apply Formula: Apply the difference of squares formula to expand $(3p - 1)(3p + 1)$ . $\newline$ $(a - b)(a + b) = a^2 - b^2$ $\newline$ $(3p - 1)(3p + 1) = (3p)^2 - (1)^2$
Simplify: Simplify $(3p)^2 - (1)^2.$ $(3p)^2 - (1)^2 = (3p \times 3p) - (1 \times 1)$ $= 9p^2 - 1$