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Hi, I'm Sean Gannis, and this is Minute Math, and
today we're learning about Binomial Square Patterns

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Minute Math, Minute Math, when we help you, Minute Math.
We have two patterns here, the Binomial Square Patterns

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a plus b all squared comes out to be
sum a squared plus 2ab plus b squared

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The second one is a minus b all squared,
that's a squared minus 2ab plus b squared

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So let's see each one of these in a practical
application. Our first one, x plus 5 all squared

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What's my a value here? a value is my x value.
My b value, the second value here, is a 5

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Analysis is a plug-and-play kind of operation.
a is x, so we have an x squared, right there

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Plus 2 times my a value,
which is x. b value, 5

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Plus the last one, b value, which is 5
all squared. And now we have to simplify

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x squared, just like that. 2 times x times 5,
multiply the 2 and 5 together, we get a 10

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We have 10x right here. And lastly,
5 squared, well, that's a 25

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And so using the binomial square
pattern, we can quickly simplify it

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x plus 5 all squared to be an
x squared plus 10x plus 25

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Now let's try a special one
here, the a minus b all squared

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Same idea, let's set my a value, that's equal to 2x,
and this is where everyone messes up a little bit

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What is my b value? Well, you want to write
negative 3y, but it's actually just 3y

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Remember, the minus sign is what's in between.
We're trying to see what will be in front here

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So that's just 3y. Following our pattern here, we
have a squared, so an a value of 2x all squared

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minus 2 times a, again, that's 2x,
times my b value, a positive 3y

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plus my last value, b squared,
which is a 3y all squared

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So now we want to simplify each part. 2x all squared,
2 times 2 is a 4, and we have an x squared here

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The next part here, 2 times 2 times 3,
well, 2 times 3 is a 4, times a 3 is a 12

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so we minus a 12 here, x, y are two variables
that are left over, plus 3y all squared

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3 squared is a 9, y squared is a y squared. And there we
have it, the second binomial, we multiply squared here

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is 4x squared minus 12xy plus 9y squared. Well, I hope
you learned something here on binomial squares patterns

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