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

Identify Form: Identify the form of the expression. The expression (3w + 3)(3w - 3) 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: Identify the values of a and b. Compare (3w + 3)(3w - 3) with (a + b)(a - b). a = 3w b = 3Apply Formula: Apply the difference of squares formula. Using the formula (a + b)(a - b) = a^2 - b^2, we get: (3w + 3)(3w - 3) = (3w)^2 - (3)^2Calculate Squares: Calculate the squares of a and b. (3w)^2 = 9w^2 (since (3w) * (3w) = 9w^2) (3)^2 = 9 (since 3 * 3 = 9)Subtract Squares: Subtract the square of b from the square of a. 9w^2 - 9

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

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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

(3w + 3)(3w - 3)

Identify Form: Identify the form of the expression. $\newline$ The expression $(3w + 3)(3w - 3)$ 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: Identify the values of $a$ and $b$ . Compare $(3w + 3)(3w - 3)$ with $(a + b)(a - b)$ . $a = 3w$ $b = 3$
Apply Formula: Apply the difference of squares formula. $\newline$ Using the formula $(a + b)(a - b) = a^2 - b^2$ , we get: $\newline$ $(3w + 3)(3w - 3) = (3w)^2 - (3)^2$
Calculate Squares: Calculate the squares of $a$ and $b$ . $\newline$ $(3w)^2 = 9w^2$ (since $(3w) \times (3w) = 9w^2$ ) $\newline$ $(3)^2 = 9$ (since $3 \times 3 = 9$ )
Subtract Squares: Subtract the square of $b$ from the square of $a$ . $9w^2 - 9$