Can this algebraic expression be simplified?

  • Thread starter MaxManus
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    Algebra
The key here is to recognize that both terms contain the factor (1-a)a, so you can factor that out and simplify.
  • #1
MaxManus
277
1
show that:
a-a(1-a)a + a1-a(1-a)a-1
can be written as:

a-a(1-a)a-1



The Attempt at a Solution



a-a(1-a)a + a1-a(1-a)a-1

a-a(1-a)a + a1a-a(1-a)a(1-a)-1

a-a(1-a)a( 1 + a(1-a)-1)
 
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  • #2
MaxManus said:
show that:
a-a(1-a)a + a1-a(1-a)a-1
can be written as:

a-a(1-a)a-1

The Attempt at a Solution



a-a(1-a)a + a1-a(1-a)a-1

a-a(1-a)a + a1a-a(1-a)a(1-a)-1

a-a(1-a)a( 1 + a(1-a)-1)

In your third line of working, instead of taking out a factor of (1-a)a, try taking out a factor of (1-a)a-1
 
  • #3
Thanks
 
  • #4
MaxManus said:
show that:
a-a(1-a)a + a1-a(1-a)a-1
can be written as:

a-a(1-a)a-1



The Attempt at a Solution



a-a(1-a)a + a1-a(1-a)a-1

a-a(1-a)a + a1a-a(1-a)a(1-a)-1

a-a(1-a)a( 1 + a(1-a)-1)

You really should get into the habit of including "=" between expessions that have the same value. If you don't, it will come back to bite you.
 
  • #5
a-a(1-a)a + a1-a(1-a)a-1

= a-a(1-a)a + a1a-a(1-a)a (1-a)-1

= a-a(1-a)a( 1 + a(1-a)-1)

Like this?
 
  • #6
Yep, that's it.
 

What is simple algebra and how is it used?

Simple algebra is a branch of mathematics that deals with manipulating symbols and equations to solve for unknown quantities. It is used in various fields such as science, engineering, and economics to model and solve real-world problems.

What are the basic rules of simple algebra?

The basic rules of simple algebra are the commutative, associative, and distributive properties. The commutative property states that the order of numbers does not affect the outcome of addition or multiplication. The associative property states that the grouping of numbers does not affect the outcome of addition or multiplication. The distributive property states that multiplying a number by a sum or difference is the same as multiplying the number by each term and then adding or subtracting the results.

How do you solve an algebraic equation?

To solve an algebraic equation, you must isolate the variable on one side of the equation. This is done by using inverse operations, such as adding, subtracting, multiplying, or dividing, to get rid of any constants or coefficients attached to the variable. The goal is to end up with a simplified expression that represents the value of the variable.

What are the common mistakes to avoid when working with simple algebra?

Some common mistakes to avoid when working with simple algebra include not following the order of operations, misinterpreting the meaning of symbols, and making arithmetic errors. It is important to pay attention to the details and carefully follow each step in the solving process to ensure accuracy.

How can I practice and improve my skills in simple algebra?

To practice and improve your skills in simple algebra, you can solve a variety of equations and word problems. There are also many online resources and textbooks available that offer practice problems and explanations. Additionally, seeking help from a tutor or joining a study group can also be beneficial.

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