Difference in expansion of brackets

In summary, expanding brackets involves multiplying out the terms within the brackets and simplifying the resulting expression. To expand brackets with two terms, the FOIL method is used. The purpose of expanding brackets is to simplify and solve more complex algebraic expressions. Brackets can be expanded with any number of terms using the same FOIL method. Expanding brackets is essentially applying the distributive property, which states that multiplying a number or variable by a sum or difference is the same as multiplying it by each term individually and then adding or subtracting the resulting products.
  • #1
mathlearn
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Let's say that there is an expression $x^2+y^2=14$

Cannot this expression be written as $(x+y)^2 = 14$ taking out the square which is common to both the terms $x$ and $y$ but after writing like that doesn't this become $x^2+2xy+y^2$=14

So writing the expression like that would it remain valid or not ?
 
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  • #2
In general, we have:

\(\displaystyle (a+b)^2\ne a^2+b^2\)

Students make this mistake so often it has been given a name...The Freshman's Dream.
 

FAQ: Difference in expansion of brackets

What is the difference between expanding brackets and simplifying expressions?

Expanding brackets involves multiplying out the terms within the brackets and simplifying the resulting expression. Simplifying expressions involves combining like terms and reducing the expression to its simplest form.

How do you expand brackets with two terms?

To expand brackets with two terms, use the FOIL method: multiply the First terms, then the Outer terms, then the Inner terms, and finally the Last terms. Then combine like terms if possible.

What is the purpose of expanding brackets?

The purpose of expanding brackets is to simplify and solve more complex algebraic expressions. It allows us to distribute a number or variable to each term within the brackets, making the expression easier to work with.

Can you expand brackets with more than two terms?

Yes, brackets can be expanded with any number of terms. Use the same FOIL method, but make sure to multiply each term by every other term within the brackets.

How does expanding brackets relate to the distributive property?

Expanding brackets is essentially applying the distributive property, which states that multiplying a number or variable by a sum or difference is the same as multiplying it by each term individually and then adding or subtracting the resulting products. In other words, expanding brackets distributes the number or variable to each term within the brackets.

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