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# Squaring binomials of the form (ax+b)²

CCSS.Math:

## Video transcript

we're asked to simplify or to expand 7x plus 10 to the second power now the first thing I will show you is exactly what you should not do what well there's a huge temptation a lot of people will look and say oh that's 7x squared plus 10 squared this is wrong and I'll write it in caps this is wrong what your brain is doing is thinking oh if I had 7x times 10 and I squared that this would be 7x squared times 10 squared we aren't multiplying here we're adding 7x to 10 so you can't just square each of these terms I just wanted to highlight this is completely this is completely wrong and to see why it's wrong you have to just remind yourself that 7x plus 10 squared this is the exact same thing as 7x Plus 10 times 7x plus 10 that's what it means to square something you're multiplying by you're multiplying it by itself well I guess twice here if you only do it once you'd only have one 7x Plus 10 so this is what it is so we're really just multiplying a binomial or two binomials they just happen to be the same one and you could use foil you could use the distributive method but this is actually a special case when you're squaring a binomial so let's just think about it as a special case first and we can apply whatever we learn to this so we could have just done it straight here but I want to learn the general case so you can apply it to any problem that you might see so if I have a plus B squared we already realize that's not a squared plus B squared that is a plus B times a plus B and now we can use the distributive property we can distribute this a plus B times this a so we get we get a times a plus B and then we could distribute the a plus B times this B plus B times a plus B and then we distribute this a we get a squared plus a B plus B times a is another a B and I'm just swapping the order so it's the same as this plus B times which is V squared these are the same or these are like terms so we can add them one of something plus another of that something will give you two of that something to a B we have a squared plus two AV plus B squared so the pattern here the pattern here if I have a plus B squared it's equal to a squared plus two times the product of these numbers plus B squared so over here I have seven X plus 10 squared so this is going to be equal to 7x squared 7 x squared plus 2 times the product of 7 x + 10 2 times 7x times 10 plus 10 squared so the difference between the right answer the wrong answer is that you have this middle term here that you probably you might have forgotten about if you did it this way and this comes out when you're multiplying all of the different combinations of the terms here and if we simplify this if we simplify it 7x squared that's 7 squared times x squared so 7 squared is 49 times x squared when you multiply this part out 2 times 7 times 10 that's 14 times 10 which is 140 and then we have our X and whether X there and then plus 10 squared so plus 100 and we are done