Factor. j^2 - 4 ______

Identify type and technique: Identify the type of expression and the appropriate factoring technique. The expression j^2 - 4 is a difference of squares because it can be written as j^2 - 2^2, which fits the form a^2 - b^2.Write in a^2 - b^2 form: Write the expression in the form of a^2 - b^2. j^2 - 4 can be written as (j)^2 - (2)^2.Apply difference of squares formula: Apply the difference of squares formula to factor the expression. The difference of squares formula is a^2 - b^2 = (a - b)(a + b). Here, a = j and b = 2. So, (j)^2 - (2)^2 = (j - 2)(j + 2).Check for errors: Check the factored expression for any possible errors. (j - 2)(j + 2) when expanded should result in the original expression j^2 - 4. (j - 2)(j + 2) = j^2 + 2j - 2j - 4 = j^2 - 4, which is the original expression.

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Math Problems

Algebra 1

Factor quadratics: special cases

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Q. Factor.

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j^2 - 4

Identify type and technique: Identify the type of expression and the appropriate factoring technique. $\newline$ The expression $j^2 - 4$ is a difference of squares because it can be written as $j^2 - 2^2$ , which fits the form $a^2 - b^2$ .
Write in $a^2 - b^2$ form: Write the expression in the form of $a^2 - b^2$ . $\newline$ $j^2 - 4$ can be written as $(j)^2 - (2)^2$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . Here, $a = j$ and $b = 2$ . $\newline$ So, $(j)^2 - (2)^2 = (j - 2)(j + 2)$ .
Check for errors: Check the factored expression for any possible errors. $\newline$ $(j - 2)(j + 2)$ when expanded should result in the original expression $j^2 - 4$ . $\newline$ $(j - 2)(j + 2) = j^2 + 2j - 2j - 4 = j^2 - 4$ , which is the original expression.