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# Structure in expressions — Harder example

Watch Sal work through a harder Structure in expressions problem.

## Want to join the conversation?

• Isn't -1 squared, +1. In the video he changed the form of the original equation to the new one with -1 squared; even though we need -1 as the result. So is this appropriate?
• Short Version \/
To address your first statement, (-1) squared would indeed equal 1. However, you are confusing (-1) squared with -(1) squared.

Long winded, rambling version \/
This confusion is a result of a devious property of exponents, as when you look at, say -2^2; you would think that the answer would be 4. However, -2 can be factored in a not so obvious manner into -1*2. Then, the exponent is applied to the positive two, leading to 4, which is then multiplied by negative one to become negative 4. The reason the exponent is applied before the multiplication of the -1 is because of the order of operations, parenthesis, exponents, multiplication/division and finally addition/subtraction. As exponents are before multiplication, and since -2^2 is also -1*2^2, thus the answer of the example is -4. If, however, parenthesis are present around the -2, then you will get 4.

• hey i am getting confused what is the difference between 3rd choice and the 4th one? it seems both of them can work
• The third one has an a squared rather than an a
• the first one seems to work tho
• At Sal says that it a difference of squares, which rules out option number one.
• What is Sal talking about
• ok so we just forget about the middle number
• we didnt really forget about it. we used it to determine that we were dealing with a 3x 3y perfect square. when you multiply it out its the same
• At , how is the 1 squared? It's not even a difference of 2 squares!
• 1 is squared because no matter how many times you multiply 1 times itself, it will always equal 1. It's a very unique number.
• can someone explain why he ignored the -2(3x)(3y)?
• wait how is 9x^2 equal to (3x)^2 ? I’m so confused 😐
• When we have exponents, we have to distribute them to each factor that we're dealing with. This is similar to when you are multiplying things, you distribute to every term ( 2*(3+x) = 2*3 + 2*x ). If you were "factoring" out an exponent of 2 from 9x^2, you would have to take it out of every term:
9x^2 = ( sqrt(9) * sqrt(x^2) )^2
= (3 * x)^2
• why not the first choice is seems right ?
(1 vote)
• "A" does not work because the coefficient before the parenthesis is a^2 so in reality it is a^2/1. When you multiply it out, you would only multiply the top and not the bottom so the bottom half would still remain as 2x-y.