Question

rewrite without parentheses and simplify. (7 - 4v)^2

Explanation:

Step1: Recall the formula for squaring a binomial

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\). Here, \(a = 7\) and \(b = 4v\).

Step2: Apply the formula

First, calculate \(a^2\): \(7^2 = 49\).
Then, calculate \(2ab\): \(2\times7\times4v = 56v\).
Next, calculate \(b^2\): \((4v)^2 = 16v^2\).
Now, substitute these into the formula: \((7 - 4v)^2 = 7^2 - 2\times7\times4v + (4v)^2\)

Step3: Simplify the expression

Substituting the values we found, we get \(49 - 56v + 16v^2\). We can also write it in standard quadratic form as \(16v^2 - 56v + 49\).

Answer:

\(16v^2 - 56v + 49\)