### Video Transcript

Given that four π₯ squared plus 24π₯ plus π is equal to π times π₯ plus π squared plus three π, work out the value of π.

So to find the value of π, we need to work out the right-hand side of the equation and see what π would be equal to. Letβs first begin by expanding this π₯ plus π squared. So we need to take π₯ plus π times π₯ plus π.

This is sometimes called the FOIL method. We multiply the first numbers together, π₯ times π₯, which is where we get F. And then the next letter in FOIL is O. So weβll multiply the outsides together, π₯ times π, which is ππ₯. Next is the letter I, so multiplying the insides together, π times π₯, which is ππ₯, and then lastly the letter L, multiplying the last together. π times π is π squared. And donβt forget to bring down the plus three π. We can combine these two middle terms. ππ₯ plus ππ₯ is two ππ₯.

Now letβs distribute the π. So we have ππ₯ squared plus two πππ₯ plus ππ squared. And then bring down the three π. So right now, we have that four π₯ squared plus 24π₯ plus π is equal to ππ₯ squared plus two πππ₯ plus ππ squared plus three π. So our leading terms are four π₯ squared on the left-hand side and ππ₯ squared on the right-hand side.

So the coefficients of π₯ squared have to be exactly the same. So this means that π must equal four. So on the right-hand side of the equation, letβs replace all of the πs with four. And now that weβve done that, we need to take two times four, which is eight. So our right-hand side of the equation is now four π₯ squared plus eight ππ₯ plus four π squared plus three π. So our first terms match, and the coefficients with our π₯ term have to match.

So on the left-hand side of the equation, we have 24π₯. And on the right, we have eight ππ₯. So 24 must be equal to eight π. And if we divide both sides of the equation by eight, we find that π must equal three. So letβs replace π with three on the right-hand side of the equation. And now we evaluate. Eight times three is 24. Three squared is nine, and then nine times four is 36. And then three times three is nine. So simplifying, we need to take 36 plus nine, which is 45. So what we have is that the four π₯ squareds match. The 24 π₯s match. So this means that π must equal 45. So our value of π is 45.