Factor. 16h^2 - 9 ______

Approach Determination: Determine the approach to factor 16h^2 - 9. We can observe that 16h^2 and 9 are both perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares method to factor the expression. Difference of squares formula: (a^2 - b^2) = (a - b)(a + b).Identify Form: Identify 16h^2 - 9 in the form of a^2 - b^2. 16h^2 can be written as (4h)^2 because 4h * 4h = 16h^2. 9 can be written as 3^2 because 3 * 3 = 9. So, 16h^2 - 9 can be rewritten as (4h)^2 - 3^2.Apply Formula: Apply the difference of squares formula to factor the expression. Using the formula (a^2 - b^2) = (a - b)(a + b), we substitute a with 4h and b with 3. (4h)^2 - 3^2 = (4h - 3)(4h + 3).

Home

Math Problems

Algebra 1

Factor quadratics: special cases

Full solution

Q. Factor.

\newline

16h^2 - 9

Approach Determination: Determine the approach to factor $16h^2 - 9$ . We can observe that $16h^2$ and $9$ are both perfect squares, and they are being subtracted from each other. This suggests that we can use the difference of squares method to factor the expression. Difference of squares formula: $(a^2 - b^2) = (a - b)(a + b)$ .
Identify Form: Identify $16h^2 - 9$ in the form of $a^2 - b^2$ . $\newline$ $16h^2$ can be written as $(4h)^2$ because $4h \times 4h = 16h^2$ . $\newline$ $9$ can be written as $3^2$ because $3 \times 3 = 9$ . $\newline$ So, $16h^2 - 9$ can be rewritten as $(4h)^2 - 3^2$ .
Apply Formula: Apply the difference of squares formula to factor the expression. $\newline$ Using the formula $(a^2 - b^2) = (a - b)(a + b)$ , we substitute $a$ with $4h$ and $b$ with $3$ . $\newline$ $(4h)^2 - 3^2 = (4h - 3)(4h + 3)$ .