Expand (mn-l)²: Converting to Addition and Multiplication Forms

To solve this problem, we will first rewrite the given expression $(mn-l)^2$ using the binomial square formula.

The formula for the square of a binomial is:

• $(a - b)^2 = a^2 - 2ab + b^2$

In the expression $(mn-l)^2$, identify $a = mn$ and $b = l$.

Apply the binomial square formula:

$(mn - l)^2 = (mn)^2 - 2(mn)(l) + l^2$

Calculate each term:

• $(mn)^2 = m^2n^2$
• $2(mn)(l) = 2mnl$
• $l^2 = l^2$

Combine these to write the expression as a sum of terms:

$m^2n^2 - 2mnl + l^2$

Next, express $(mn-l)^2$ as a multiplication:

By definition, the square of a term can be rewritten as the term multiplied by itself:

$(mn-l)^2 = (mn-l)(mn-l)$

Therefore, the expression rewritten as an addition and a multiplication is:

$m^2n^2-2mnl+l^2$

$(mn-l)(mn-l)$