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

Recognize pattern: Recognize the pattern in the expression (a + 3)(a - 3). This expression is in the form of (a + b)(a - b), which is a difference of squares. Difference of squares special case: (a + b)(a - b) = a^2 - b^2Identify values: Identify the values of a and b. In the expression (a + 3)(a - 3), a is simply a, and b is 3.Apply formula: Apply the difference of squares formula to the expression (a + 3)(a - 3). Using the formula (a + b)(a - b) = a^2 - b^2, we get: (a + 3)(a - 3) = a^2 - 3^2Calculate squares: Calculate the squares of a and 3. a^2 remains as a^2 since we cannot simplify it further without knowing the value of a. 3^2 is 9. So, (a + 3)(a - 3) = a^2 - 9Write final form: Write the final simplified form of the product. The product (a + 3)(a - 3) simplifies to a^2 - 9.

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Math Problems

Algebra 1

Multiply two binomials: special cases

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Q. Find the product. Simplify your answer.

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(a + 3)(a - 3)

Recognize pattern: Recognize the pattern in the expression $(a + 3)(a - 3)$ . This expression is in the form of $(a + b)(a - b)$ , which is a difference of squares. Difference of squares special case: $(a + b)(a - b) = a^2 - b^2$
Identify values: Identify the values of $a$ and $b$ . In the expression $(a + 3)(a - 3)$ , $a$ is simply $a$ , and $b$ is $3$ .
Apply formula: Apply the difference of squares formula to the expression $(a + 3)(a - 3)$ . $\newline$ Using the formula $(a + b)(a - b) = a^2 - b^2$ , we get: $\newline$ $(a + 3)(a - 3) = a^2 - 3^2$
Calculate squares: Calculate the squares of $a$ and $3$ . $a^2$ remains as $a^2$ since we cannot simplify it further without knowing the value of $a$ . $3^2$ is $9$ . So, $(a + 3)(a - 3) = a^2 - 9$
Write final form: Write the final simplified form of the product. $\newline$ The product $(a + 3)(a - 3)$ simplifies to $a^2 - 9$ .