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> 71^2

Accepted Answer

Welcome back. I am so glad you're here. We are given the numbers 94 squared and we're asked to find the product of the two numbers. The two numbers were finding the product of our 94 times 94. But we're supposed to use the concept of special products namely X minus y squared, which is equal to x squared minus two, X, Y plus y squared. So how do we do this? Well we could think of as being -6 And then that would be squared because if we started doing what's in the parentheses first we'd have 100 -6 which is squared. But now we can identify when it's two different numbers. 106. We can identify an X X equals 100 a Y Y equal six. And now we can substitute for X and y. On the right hand side of this equation over here. So X squared, X is 100 so 100 squared minus two times X is 100 times y is six Plus. Why squared? Well that's six squared. OK, now we can simplify that a bit. So 100 square, that's 10,000 -2 times. 100 is 200 times six is plus six squared is 36. Alright, so we've got 10,000 minus 1,210,000 minus 1200 is 8800 plus 36. 8800 plus 36 equals 8836. And that's pretty cool. We could do that math in our heads. We don't need to use a calculator or need to write out 94 times 94 do the multiplication. We look at our answer choices in this matches with answer choice a 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. < SEE SAMPLE B> 71^2