Question

Find the product. $$(-5-4 x)^{2}$$

Short answer

The product of the expression \((-5-4x)^2\) is \(25 - 40x + 16x^2\).

Step-by-step solution

Understand the Binomial Squaring

The formula to square a binomial (\(a - b\)) is given by \((a - b)^2 = a^2 - 2ab + b^2\). Here in the problem, the term \(-5\) corresponds to \(a\) and the term \(-4x\) corresponds to \(b\).

Substitute the values

Now, subtitute the values of \(a\) and \(b\) into the formula. Thus the expression becomes: \((-5)^2 - 2*(-5)*(-4x) + \((-4x)^2\).

Simplify the expression

Now, simplify the expression. \((-5)^2\) becomes \(25\), \(-2*(-5)*(-4x)\) becomes \(40x\) and \((-4x)^2\) becomes \(16x^2\). Therefore, the final expression is \(25 - 40x + 16x^2\).