Question
In Exercises $31-40,$ factor the difference of two squares.$$x^{2}-144$$
In Exercises $31-40,$ factor the difference of two squares. $$x^{2}-144$$
Answers
Factor the difference of two squares.
$$x^{2}-144$$
All right. Looking at factoring the difference of two squares. Um, I'm gonna go ahead and show you the pattern that we're working with. That's a plus B multiplied by a minus, bi. It's gonna equal a squared minus B squared. All right, so that's the pattern we're approaching knowing that a squared minus B squared is what they're giving us. So our goal is to get back to to buy no meals multiplied by each other. We already know that the sign has to be different. So one of them plus one of the minus and all we're looking for is what terms to put where we'll normally we take this a squared, minus B squared number thinking the square root gives us the answer for the A square root gives us the answer for B, and that's exactly what we're going to do here. Even with a coefficient of X squared, we're gonna take the square root of both of these terms. So the square to 36 66 the squared of X squared is X, so we're actually gonna leave six x six x Then we're gonna look at the 49 take the square to that which is gonna be a seven. And that right there is your answer. Six X plus seven multiplied by a six x minus seven that is factoring the difference of square by no meal to to buy no meals right there.
All right, looking at 36 x squared minus 49 y squared in Our goal is the factor. So when we're factoring a binomial looking to factor it, too? Uh, first degree by no meals in our pattern as mentioned before it's a squared minus B squared will always turn into a plus B times a minus bi, which should be the square root of those two terms in the square root of that and will always be plus or minus. So we can already put the plus or minus in and a problem for us. Looking at the square root of 36 X squared square to 36 66 squared of X squared is X. We get the second term squared a 49 y squared square to 49. It's seven in the squared of y squared is why that gives us six x for seven. Why? Times six X minus seven. Why? And that right there is factory that by no male using the difference of two squares
I guess so. We want to find a good of falling. So let's no got 36. Weaken, right As a perfect square, that's six words. Sort of six. Extra power to on 49 is seven squared For here. We have a difference of two squares, so we can factor this into a six x minus seven times your six x plus oven.
All rights we won't affect or this using the difference of squares and just a reminder. A difference of squares is anything that takes the form a squared minus B squared, which can be rewritten as a plus B times a minus bi. So going back to our expression, me see, the X squared is already in the form a squared, and we know that four is a perfect square. It's the same as two squares. We're gonna rewrite that as two squared to put it in this form. So now that we have that, we can just follow the same template. So this is equal to X plus two times X minus two, and that's our answer.