Video Transcript
Use the distributive property to calculate the value of 76 squared plus 76 times 25 minus 76.
We’re given the expression 76 squared plus 76 times 25 minus 76. If we look at the terms we have here, we have 76 squared as our first term, 76 times 25 as our second term, and negative 76 as our third term. All three of these terms have a common factor of 76.
Using the distributive property, we can undistribute that shared factor. If we remove a factor of 76 from 76 squared, we’ll be left with 76. If we remove a factor of 76 from 76 times 25, we’ll just be left with 25.
The last term we have to be a bit more careful with. We need to say what times 76 will equal negative 76. And that is negative one. If you remove a factor of 76 from negative 76, you get negative one; you do not get zero.
Our new equivalent expression is then 76 times 76 plus 25 minus one. I might choose to take the 76 and subtract one to get 75. And 75 plus 25 equals 100. This means the value inside the parentheses is 100. And we need to multiply 76 by 100. When we do that, we get 7,600.
