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

Identify Form of Expression: Identify the form of the expression. The expression (3t + 1)(3t - 1) is in the form of (a + b)(a - b), which is a difference of squares. Special case: (a + b)(a - b) = a^2 - b^2Identify Values of a and b: Identify the values of a and b. Compare (3t + 1)(3t - 1) with (a + b)(a - b). a = 3t b = 1Apply Difference of Squares Formula: Apply the difference of squares formula. Using the values of a and b, we apply the formula (a + b)(a - b) = a^2 - b^2. (3t + 1)(3t - 1) = (3t)^2 - (1)^2Simplify the Expression: Simplify the expression. (3t)^2 - (1)^2 = (3t * 3t) - (1 * 1) = 9t^2 - 1

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

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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

(3t + 1)(3t - 1)

Identify Form of Expression: Identify the form of the expression. $\newline$ The expression $(3t + 1)(3t - 1)$ is in the form of $(a + b)(a - b)$ , which is a difference of squares. $\newline$ Special case: $(a + b)(a - b) = a^2 - b^2$
Identify Values of $a$ and $b$ : Identify the values of $a$ and $b$ . Compare $(3t + 1)(3t - 1)$ with $(a + b)(a - b)$ . $a = 3t$ $b = 1$
Apply Difference of Squares Formula: Apply the difference of squares formula. $\newline$ Using the values of $a$ and $b$ , we apply the formula $(a + b)(a - b) = a^2 - b^2$ . $\newline$ $(3t + 1)(3t - 1) = (3t)^2 - (1)^2$
Simplify the Expression: Simplify the expression. $\newline$ $(3t)^2 - (1)^2 = (3t \times 3t) - (1 \times 1) = 9t^2 - 1$