Question

Find the product. $$(x-5)(x-4)$$

Short answer

Therefore, the product of \((x - 5)(x - 4)\) is \(x^2 - 9x + 20\).

Step-by-step solution

Multiply the First Terms

We will multiply the first terms in each parenthesis together, i.e. \(x \) from \(x - 5\) and \(x \) from \(x - 4\), to get \(x^2 \). So, \(x \cdot x = x^2 \).

Multiply the Outer Terms

Next, we multiply the outer terms together, i.e. \(x \) from \(x - 5\) and \(-4 \) from \(x - 4\), to get \(-4x\). So, \(x \cdot -4 = -4x \).

Multiply the Inner Terms

Now, we multiply the inner terms together, i.e. \(-5 \) from \(x - 5\) and \(x \) from \(x - 4\), to get \(-5x\). So, \(-5 \cdot x = -5x \).

Multiply the Last Terms

Then, we multiply the last terms together, i.e. \(-5 \) from \(x - 5\) and \(-4 \) from \(x - 4\), to get \(20\). So, \(-5 \cdot -4 = 20 \).

Sum the Terms

Finally, we will add all the terms obtained from the first to the last steps together. This gives \(x^2 - 4x - 5x + 20\), which simplifies to \(x^2 - 9x + 20\).