question\nfactor completely\n36u² - 64

Answer

Explanation:

Step1: Factor out the GCF

First, find the greatest - common factor of 36 and 64. The GCF of 36 and 64 is 4. $36u^{2}-64 = 4(9u^{2}-16)$

Step2: Recognize the difference of squares

The expression $9u^{2}-16$ is a difference of squares, since $9u^{2}=(3u)^{2}$ and $16 = 4^{2}$. The formula for the difference of squares is $a^{2}-b^{2}=(a + b)(a - b)$. Here, $a = 3u$ and $b = 4$. $9u^{2}-16=(3u + 4)(3u - 4)$

Step3: Write the completely factored form

Substitute the factored form of $9u^{2}-16$ back into the expression from Step 1. $4(9u^{2}-16)=4(3u + 4)(3u - 4)$

Answer:

$4(3u + 4)(3u - 4)$