Question

multiply. assume that all variables represent positive real numbers.
$(sqrt{j} - q)(sqrt{j} + q)$

Explanation:

Step1: Apply difference of squares formula

The expression \((\sqrt{j}-q)(\sqrt{j}+q)\) is in the form of \((a - b)(a + b)\), where \(a=\sqrt{j}\) and \(b = q\). The difference of squares formula is \((a - b)(a + b)=a^{2}-b^{2}\).
So, substituting \(a=\sqrt{j}\) and \(b = q\) into the formula, we get \((\sqrt{j})^{2}-q^{2}\).

Step2: Simplify \((\sqrt{j})^{2}\)

By the property of square roots, \((\sqrt{x})^{2}=x\) for \(x\geq0\). Since \(j\) is a positive real number (given that all variables represent positive real numbers), \((\sqrt{j})^{2}=j\).

So the simplified form of \((\sqrt{j})^{2}-q^{2}\) is \(j - q^{2}\).

Answer:

\(j - q^{2}\)