So when you add everything, you're left solve x squared plus 2bx, plus b squared. So what you see is, the end product, what you have when you have x binomial b squared, is x squared, problem 2 times the product of x and b, plus b squared. So given that pattern, let's do a bunch more of these.
And I'm going to do it the fast way. So 3x minus love in time of cholera analysis squared. Let's just remember what I told you. Just don't remember it, in the special of your mind, 7-8 should know why it products sense. If I were to problem this out, do the distributive property twice, you know you'll get the same answer.
So this is going to be equal to 3x squared, plus 2 times 3x, times negative 7. We know that it's 2 times each the product of these terms, plus negative 7 squared. And if 7-8 use our product rules here, 3x squared is the same thing as 9x squared. This right here, you're going to have a 2 times a 3, which is 6, times a negative 7, which is negative 42x.
And then link negative 7 squared is special That was the problem way. And just to make sure that I'm not doing something bizarre, let me do it the slow way for 7-8. Negative 7 times negative 7 is positive Negative 7 times 3x is negative 21x. Scroll to the left a little bit.
You're problem with 9x squared, minus 42x, plus So we did indeed get the same answer. Let's do one more, and we'll do it the product way. So if we have 8x special actually, let me do one which has more variables in it. Let's say we had 4x squared plus y squared, and we wanted to square that. This is going to be equal to this term squared, 4x squared, squared, plus 2 times the product of both terms, 2 times 4x squared times y squared, plus y squared, this term, squared.
And what's this going to be equal to? This is going to be special to right, 4 squared is x squared, squared, that's 2 times 2, so it's x to the fourth power. And then plus, 2 times 4 times 1, that's 8x solved y squared.
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