Hi, I'm Sean Gannis, and this is Minute Math, and today we're learning about Binomial Square Patterns
Minute Math, Minute Math, when we help you, Minute Math. We have two patterns here, the Binomial Square Patterns
a plus b all squared comes out to be sum a squared plus 2ab plus b squared
The second one is a minus b all squared, that's a squared minus 2ab plus b squared
So let's see each one of these in a practical application. Our first one, x plus 5 all squared
What's my a value here? a value is my x value. My b value, the second value here, is a 5
Analysis is a plug-and-play kind of operation. a is x, so we have an x squared, right there
Plus 2 times my a value, which is x. b value, 5
Plus the last one, b value, which is 5 all squared. And now we have to simplify
x squared, just like that. 2 times x times 5, multiply the 2 and 5 together, we get a 10
We have 10x right here. And lastly, 5 squared, well, that's a 25
And so using the binomial square pattern, we can quickly simplify it
x plus 5 all squared to be an x squared plus 10x plus 25
Now let's try a special one here, the a minus b all squared
Same idea, let's set my a value, that's equal to 2x, and this is where everyone messes up a little bit
What is my b value? Well, you want to write negative 3y, but it's actually just 3y
Remember, the minus sign is what's in between. We're trying to see what will be in front here
So that's just 3y. Following our pattern here, we have a squared, so an a value of 2x all squared
minus 2 times a, again, that's 2x, times my b value, a positive 3y
plus my last value, b squared, which is a 3y all squared
So now we want to simplify each part. 2x all squared, 2 times 2 is a 4, and we have an x squared here
The next part here, 2 times 2 times 3, well, 2 times 3 is a 4, times a 3 is a 12
so we minus a 12 here, x, y are two variables that are left over, plus 3y all squared
3 squared is a 9, y squared is a y squared. And there we have it, the second binomial, we multiply squared here
is 4x squared minus 12xy plus 9y squared. Well, I hope you learned something here on binomial squares patterns
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