Hello wonderful mathematics people. I'm Anna Cox from Kella Community College. Difference of squares a ^2 -, b ^2 factors into a -, b * a + b. Now it doesn't matter which order we multiply in because we have the commutative properties. So it could be a + b * a -, b. So when we look at a problem that's only got 2 terms, IEA binomial, if the first term is a square and the second term is a square, it will always factor into the first term plus the second, and the first term minus the second, the square root of the X ^2 and the square root of the 9. So X + 3 X -3. If you thought about foiling it, your outside terms and inside terms will cancel. 3 * -3 is the -9 X times X is the X ^2. This next 14Y squared is a perfect square. It's four y * 4 Y. So the four y * 4 Y, it's a minus. So one's going to be a + 1's going to be a -. 25 is also a perfect square, so five and five. And that's factored. If we look at a more complex 1, is 81 a perfect square 9 * 9? How about A to the 4th a ^2 * a ^2 b ^2 B * b is 49 a perfect square? Yes, 7 * 7 C to the 8th, C to the fourth times, C to the 4th. So this really is the difference of squares where nine a ^2 b * 9 A squared B would give me the 81 A to the 4th b ^2. One's going to be a minus and one's going to be a plus, doesn't matter which location. And seven C to the fourth times 7 C to the fourth would give me 49 C to the 8th. We also have perfect square trinomials and a perfect square trinomial is in the form a ^2 -, 2 AB plus b ^2, which factors into the quantity a -, b ^2. Also a ^2 + 2 AB plus b ^2 factors into the quantity a + b ^2. So 40 nine y ^2 -, 14 Y plus 149 Y squared. This is a perfect square In the front one is also a perfect square. And the question becomes if we have seven y -, 1 and we square it, if we multiply these two terms, outer terms, seven y * -1 and double it, does that give us the -14 Y? And the answer is yes. Now, sometimes we have to look to see that there's a greatest common factor before we ever start. What number can come out of 3248 and 18? We're going to pull A2 out and we're going to get 16 X squared plus 24X plus 916 X squared's a perfect square and 9's a perfect square. So if we think about sqrt 16 X squared is 4 X sqrt 9's 3. So four X * 312 X, when we double that, that's that middle term of 24X. So we know that this is going to factor into two times the quantity of four X + 3 ^2. This next one we have a two that will come out and we get four X ^2 -, 20 X plus 25. Well, four X squared's a perfect square, 25 is a perfect square. And if we thought about two X from the front and five from the back, multiply them, that's 10X. And if we doubled it, we would get the 20. We have to pay attention to the sign here. So it's going to be a -, 5 because -5 * -5 is +25 and -10 X plus -10 X when we foil would give us that -20 X. Thank you and have a wonderful day. This is Anna Cox.