Question

Find the product. $$ (d-5)(d+3) $$

Short answer

\(d^2-2d-15\)

Step-by-step solution

First terms

Multiply the first terms in each binomial. In this case, multiply \(d\) and \(d\) to get \(d^2\).

Outer terms

Next, multiply the outer terms in the binomial expression. Here multiply \(d\) (from the first binomial) and \(3\) (from the second binomial) to get \(3d\).

Inner terms

Now, multiply the inner terms. That means multiply \(-5\) (from the first binomial) and \(d\) (from the second binomial) to get \(-5d\).

Last terms

Then, multiply the last terms of each binomial. Here multiply \(-5\) and \(3\) to get \(-15\).

Combine like terms

After completing steps 1-4, obtain \(d^2+3d-5d-15\). Next combine like terms that are the terms with the same variable and order, in this case \(3d\) and \(-5d\), to simplify the expression to \(d^2-2d-15\).