Question

factor completely. 45w² - 80w⁴

Explanation:

Step1: Find GCF of coefficients and variables

The coefficients are 45 and 80. GCF of 45 and 80 is 5. For variables, the lowest power of \( w \) is \( w^2 \). So GCF is \( 5w^2 \). Factor out \( 5w^2 \):
\( 45w^2 - 80w^4 = 5w^2(9 - 16w^2) \)

Step2: Factor the difference of squares

Notice \( 9 - 16w^2 \) is a difference of squares (\( a^2 - b^2 = (a - b)(a + b) \)), where \( a = 3 \), \( b = 4w \). So:
\( 9 - 16w^2 = (3 - 4w)(3 + 4w) \)

Step3: Combine factors

Substitute back the factored form of \( 9 - 16w^2 \) into the expression:
\( 5w^2(3 - 4w)(3 + 4w) \)

Answer:

\( 5w^2(3 - 4w)(3 + 4w) \)