Question

factor completely.
50 - 72w²

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of 50 and 72. The GCF of 50 and 72 is 2. Factor out 2 from the expression:
$$50 - 72w^2 = 2(25 - 36w^2)$$

Step2: Apply difference of squares

Notice that \(25 - 36w^2\) is a difference of squares, since \(25 = 5^2\) and \(36w^2=(6w)^2\). The formula for difference of squares is \(a^2 - b^2=(a + b)(a - b)\). Here, \(a = 5\) and \(b = 6w\), so:
$$25 - 36w^2=(5 + 6w)(5 - 6w)$$

Step3: Combine the factors

Substitute the factored form of \(25 - 36w^2\) back into the expression from Step 1:
$$2(25 - 36w^2)=2(5 + 6w)(5 - 6w)$$

Answer:

\(2(5 + 6w)(5 - 6w)\)