Simplify −13+4x+x(9−x)-13+4x+x\left(9-x\right)−13+4x+x(9−x)

−x2+13x−$$13-x^2+13x-13$$−x2+13x−13

Simplify − 13 + 4 x + x ( 9 − x ) -13+4x+x\left(9-x\right) − 13 + 4 x + x ( 9 − x )

Alright, folks, let's keep moving along with another practice problem. So, we have to simplify this algebraic expression negative 13+4x+x it gets multiplied into 9 minuteus x So, notice here in this problem, I have some constants like -13, but I also have some variables like 4x or x that gets multiplied into another expression with x. So let's just take it from the top. The first thing we have to do is we have to distribute any constants or variables into or through your parentheses, if you have any. And we do. So let's go ahead and start with that first. If I multiply the x into the 9 minuteus x, what do I get? Well, x times 9 is just 9 x. But what about x times negative x? Well, this actually ends up being minus x times x And remember, from our rules of exponents or our exponents here we can actually just rewrite this as x to the second power or x squared. Alright? So this is what that expression ends up becoming. So now I have the 4 x on the outside here, and I'm gonna rewrite the negative 13. Alright? So this is negative 13 plus, all this stuff. So here I've got the negative 13 and which is a constant. I've got some terms that now have one power of x, but now I have a new kind of term, which is an x squared or x to the second power. Alright? So let's go ahead and start with this next step here, which is grouping together the like terms. I have to group all the things that are similar to each other. So do I group these things together because they're similar? Well, no. Because remember, like terms are gonna be terms to the same power. And this x squared and this 9x and 4x, they're similar, but they're not like terms because they have a different power. Alright? So I need to group together the like terms, and I'm gonna I'm gonna rewrite this just in terms of decreasing exponents. So negative x squared, that goes first. I move the negative sign over then the, the 4x and the 9x just become, you know, 4x and 9x they're together And notice I'm keeping the signs. And now, I have the negative 13 on the outside. So this just ends up being negative 13 over here on the outside. And notice how I actually didn't really do anything. These were already grouped together, to be very similar. So all I have to do now is just start with the next step, which is finish off by combining the like terms. Alright? So this actually just ends up being negative x squared. The 4x and the 9x actually become plus 13x, and then I have minus 13 on the other side. Alright? So in other words, this is basically what my expression has become. So I've got, in decreasing order of exponent, which is usually the way that you're gonna see it. Alright? So, again, this complicated expression becomes just an expression with 3 terms, and we've simplified it. That's all there is to it. Let me know if you have any questions.