Identify type of factoring: Identify the type of factoring required for the expression 9j^2 - 16. The expression is a difference of squares because it is in the form a^2 - b^2, where 9j^2 is the square of 3j and 16 is the square of 4.Write as difference of squares: Write the expression 9j^2 - 16 as a difference of squares. 9j^2 = (3j)^2 and 16 = 4^2, so 9j^2 - 16 can be written as (3j)^2 - 4^2.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). Using this formula, we get (3j)^2 - 4^2 = (3j - 4)(3j + 4).Check for errors: Check the factored expression for any possible errors. (3j - 4)(3j + 4) when expanded should result in the original expression 9j^2 - 16. Let's expand it to verify: (3j - 4)(3j + 4) = 9j^2 + 12j - 12j - 16 = 9j^2 - 16, which matches the original expression.

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor

9j^2 - 16

Identify type of factoring: Identify the type of factoring required for the expression $9j^2 - 16$ . The expression is a difference of squares because it is in the form $a^2 - b^2$ , where $9j^2$ is the square of $3j$ and $16$ is the square of $4$ .
Write as difference of squares: Write the expression $9j^2 - 16$ as a difference of squares. $\newline$ $9j^2 = (3j)^2$ and $16 = 4^2$ , so $9j^2 - 16$ can be written as $(3j)^2 - 4^2$ .
Apply difference of squares formula: Apply the difference of squares formula to factor the expression. $\newline$ The difference of squares formula is $a^2 - b^2 = (a - b)(a + b)$ . Using this formula, we get $(3j)^2 - 4^2 = (3j - 4)(3j + 4)$ .
Check for errors: Check the factored expression for any possible errors. $\newline$ $(3j - 4)(3j + 4)$ when expanded should result in the original expression $9j^2 - 16$ . Let's expand it to verify: $\newline$ $(3j - 4)(3j + 4) = 9j^2 + 12j - 12j - 16 = 9j^2 - 16$ , which matches the original expression.