Question

find the product.
$-(7x - 2)^2$
the answer is \boxed{}.
(simplify your answer.)

Explanation:

Step1: Recall the square of a binomial formula

The formula for \((a - b)^2\) is \(a^2 - 2ab + b^2\). Here, \(a = 7x\) and \(b = 2\). So, \((7x - 2)^2=(7x)^2-2\times(7x)\times2 + 2^2\).

Step2: Expand the square

Calculate each term: \((7x)^2 = 49x^2\), \(2\times(7x)\times2 = 28x\), and \(2^2 = 4\). So, \((7x - 2)^2 = 49x^2 - 28x + 4\).

Step3: Apply the negative sign

We have \(-(7x - 2)^2\), so multiply the expanded form by \(-1\): \(-1\times(49x^2 - 28x + 4)=-49x^2 + 28x - 4\).

Answer:

\(-49x^2 + 28x - 4\)