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 A> x = 63 y = 57

Accepted Answer

Welcome back. I am so glad you're here. We are given two numbers 34 times 26 we're asked to find their product to multiply them. Except we are supposed to use the concept of special products namely that X plus Y, times X minus Y equals x squared minus Y squared. Okay, how do we get from the left side to the right side? Well, they both have two things being multiplied by each other. 34 could be this first one and 26 could be the second one. And how could we rewrite 34 as X plus Y and 26 as X minus Y. Well, we need to numbers that when added together equal 34 when subtracted from each other equal 26. So for the first number, that should probably be something right in the middle of 36. So if we take 30 And add four, that does equal 34. And then we need to take those same two numbers and subtract them. Well, 30 minus four, that does equal 26. And now we can identify an X and a Y. And then go back in and plug them in on the right hand side. So X. Is the first one X equals 30. Why is the second one? Y equals four. So on the right hand side of the equation we have X squared, that's 30 squared minus why squared? Why is four? So four squared? Now we can simplify that. 30 squared is 900 minus four squared four squared is 16. So 900 minus 16 equals 884. That's a pretty cool way to solve 34 times 26. We look at our answer choices and that matches with answer choice D. Well done, we'll catch you on the next one.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

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. x = 63 y = 57