Factor the following completely: Ifit cannot be factored, write PRIMEab + Sa - b - 52) x_13x + 36...

Factor completely. $(a+b)^{2}-36$

It in this problem, we want to factor an expression by using the perfect square. Try no meal. So let's take a look at 25 A squared plus 60 A. B. Plus 36 B squared. Now on this problem here, if it's a perfect square, try no meal, let's take the 1st and 3rd term and check to make sure they are perfect squares. The square 2 25 A. Square does five A. And the square root of 36 B squared is six B. So let's multiply six. b and 58 together and then double it. If this doubled, makes this middle term 60 A. B. Then we have a perfect square. Try no meal, 60 times five days, 30 A. B. And double it. You get 68 B. So that worked out Now we know that five a and 60 our our term our our help help us make our Bino meals. So let's use our plus sign here on this middle term as well. five A plus 60 times five A plus six B. And together we can put those together by using a power five A plus 60 square

Yeah, we are given the polynomial six a squared he squared plus 18. Hey, be cube and we were asked to completely factor this polynomial. It's important to keep in mind that factoring is the opposite of distribution. So what that means our final answer is going to look like a problem. We would be asked to distribute the greatest common factor. The factor in common between these two mano meals is what's gonna go outside bar parentheses. So let's take this step by step first. What is the greatest common factor of six and 18? That is six. No, looking at a squared and A to find the greatest common factor of variables. We want to take the variable with the lower exponents because that's what shared in common between the two. So this is an imaginary 18 of the first, so we're just gonna take eight of the first as our greatest common factor. And then, lastly, we have B squared and be cute. Well, in common is that lower exponents, which is a B squared. So that's what's in common between these two mano meals. Now, distributing means we need to multiply out. So the factor we're gonna do the opposite of multiplication and we're gonna divide our original polynomial by our greatest common factor. Let's do this one by one. Dividing here 1st 6 divided by six is one a squared, divided by a Remember this, an imaginary one will be Divide variables. We subtract the exponents. So two minus one gives us eight of the first power and then b squared, divided by B squared. Anything divided by itself is one. So our be variable will be eliminated. No doing division here. 18 divided by six. Well, that's three. A divided by a again, a number divided or anything divided by itself is one. So they will be eliminated and be cubed. Divided by B squared is just be to the 1st 3 minus two is one This right here we have just created is our fully factored form of our original polynomial

This problem involves factoring a what appears to be complex. Try no meal, but what we can do right off the bat when what stands out to me is, Each of these terms has an A plus B in it, so I can factor out an A plus B from each of those terms and leave me with a new, simpler try no meal X squared minus 13 X plus 36. So this is my new polynomial might try no meal that I need to factor and I'm gonna use the product some method. So something that multiplies two factors that multiply to give you 36 add to give you negative 13. So when I think of 36 you can go 36 times one that won't get you there. You could go won't get you to 13. You could go 12 times three. That still won't get you to 13, but I could also use nine times four. Now what you notice nine times four equals 36 9 plus four is 13, but I needed to equal negative 13 so I can throw two negatives on this because the negative times a negative still gives you a positive and negative nine plus negative four equals negative. 13. So those are my two factors. Negative nine Negative four. So let's write this out in completed form of the A plus B, and then they'll be X minus nine and x minus four.

Telephones we have to do the factor of this given expression that is three A. B. Square minus six Maybe the spell? Maybe two. Yeah. Okay so we by inspecting the of transporting easter we determined that each contents effect roles of transporting. He's done really to remind that each contents each convince three mm. And the mhm. Each condense effect laws three A. N. B. So the greatest conflict er is so therefore the greatest conflict. The greatest conflict carriage. Three A. B. So we can write this means that three A. B squared minus six amy plus 12 of a BQ. Your question three A. B. Off B minus three A. B. Tens of two. Yes three maybe there was four. We square. Okay so we can idea to the baby we will take common three V. From eastern so this will be minus two. Bless all we square. So this is the answer I hope you understood. Thank you.