### Video Transcript

Find π΄π΅ given that π΄ equals eight π₯ plus two and π΅ equals five π₯ minus one.

π΄π΅ will be found by multiplying the expression π΄ times the expression for π΅, eight π₯ plus two times five π₯ minus one. Weβll need to expand this multiplication. We multiply the first two terms, eight π₯ times five π₯, then the outer two terms, eight π₯ times negative one. Make sure that you bring that negative with the one value. Itβs not eight π₯ times one. Itβs eight π₯ times negative one.

For now, we multiply the insides, two times five π₯, and then the lasts, two times negative one. Again make sure you carry that negative one down, two times negative one. And then, weβll add all four of these terms.

First, weβll multiply the coefficients. Eight times five equals 40. We have the π₯-variable. And we add the two exponents. π₯ times π₯ equals π₯ squared, π₯ to the one plus one power. Eight π₯ times five π₯ equals 40π₯ squared. This time, weβll multiply eight by negative one, which is negative eight. And we have one π₯-variable. The same thing for two times five π₯. Weβll multiply two times five, which is 10, and bring down the π₯. For the final term, two times negative one equals negative two. And weβre trying to combine these terms together.

We now need to look and see if any of these terms can be combined. You can combine terms who have the same variable and the same exponent. Negative eight π₯ can be added to 10π₯. You can imagine negative eight π₯ as eight negative π₯ terms. And you can imagine 10π₯ as 10 positive π₯ terms. When you add a negative and a positive together, they cancel out. And that means negative eight π₯ plus 10π₯ leaves us with two π₯, two positive π₯ values. We bring down the 40π₯ squared, which hasnβt changed, and the negative two, which hasnβt changed.

And we can say that π΄π΅ equals 40π₯ squared plus two π₯ minus two.