The special products can be used to perform selected multiplicati...

Question

The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2. On the right, (x-y)^2 = x^2-2xy+y^2. Use special products to evaluate each expression. <SEE SAMPLE B> 102^2

Accepted Answer

Welcome back. I am so glad you're here. We are given this number 67 squared and asked to find the product of two numbers. The two numbers were asked to find the product of our 67 times 67 or 67 squared but were asked to use the concept of special products namely that x minus y squared equals x squared minus two X Y plus y squared. So what does this mean? Well, it means we're going to replace this X -Y. What's in here? And we're going to look at two numbers for 67. That could be rewritten as 70 - because following penned as we recall from previous lessons, we do what's in the parentheses First we do 70 minus three. So that would be 67 squared. But now we can identify an X and a Y and plug those in for the exes. And wise on the right hand side of the equation. So X is the first one, so X equals 70. And why is the 2nd 1? So why equals three. Now we can rewrite the right hand side, X squared, That's 70 squared minus two times X is 70 times y is three plus Y squared. That's three squared. Now we can simplify, 70 squared is going to be -2 times 70 is 100 3 would be 420 plus three squared while three squared is nine. Now we can combine this 4900 minus 420 is going to leave us with 4480 plus nine and now we can do that addition. We have 4489 and that's a pretty cool way to solve it. We can do that in our heads without a calculator or without writing it out 67 times 67. We look at our answer choices and 4,489 matches with answer choice b. Well done, we'll catch you on the next one.

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The special products can be used to perform selected multiplications. On the left, we use (x+y)(x-y) = x^2-y^2. On the right, (x-y)^2 = x^2-2xy+y^2. Use special products to evaluate each expression. 102^2