Question

rewrite without parentheses and simplify.
$(5 - 3w)^2$

Explanation:

Step1: Apply the square of a binomial formula

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\). Here, \(a = 5\) and \(b = 3w\). So we have:
\[
(5 - 3w)^2 = 5^2 - 2\times5\times(3w)+(3w)^2
\]

Step2: Calculate each term

• Calculate \(5^2\): \(5^2 = 25\)
• Calculate \(2\times5\times(3w)\): \(2\times5\times3w = 30w\)
• Calculate \((3w)^2\): Using the power of a product rule \((ab)^n=a^n b^n\), we get \((3w)^2 = 3^2\times w^2 = 9w^2\)

Step3: Combine the terms

Substitute the calculated values back into the formula:
\[
25 - 30w + 9w^2
\]
We can also write it in standard polynomial form: \(9w^2 - 30w + 25\)

Answer:

\(9w^2 - 30w + 25\) (or \(25 - 30w + 9w^2\))