Expand and Simplifying Algebraic Expressions

In summary, to expand and simplify the given algebraic expression, first use the FOIL method to multiply the first two factors. Then, multiply the result by the third factor using either horizontal or vertical method. Finally, apply the Distributive Law and collect like terms to simplify the expression.
  • #1
madeleine_123
1
0

Homework Statement



Expand and simplify algebraic expressions.

Homework Equations



(2a+1)(3a-1)(a-2)

The Attempt at a Solution



The problem is, we normally always do these problems with only two sets of brackets. I tried just multiplying each number will each other number but it didn't work.
 
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  • #2
madeleine_123 said:

Homework Statement



Expand and simplify algebraic expressions.

Homework Equations



(2a+1)(3a-1)(a-2)

The Attempt at a Solution



The problem is, we normally always do these problems with only two sets of brackets. I tried just multiplying each number will each other number but it didn't work.
Multiply the first two factors by the FOIL method. Then multiply the result by the third factor, either horizontally or vertically.
 
  • #3
madeleine_123 said:
(2a+1) · (3a-1)(a-2)
You say you know how to simplify what's in blue? So go ahead and do that.

Next, remember you are actually using the Distributive Law for this, and it says the above is equal to:

2a · (3a-1)(a-2) + 1 · (3a-1)(a-2)

So when you have worked out a simpler expression for what's in blue, write it in place of what I've shown in blue and perform the above multiplications, then collect like terms to simplify.
 

1. What does it mean to expand an algebraic expression?

Expanding an algebraic expression involves multiplying out the terms and simplifying the resulting expression. This is often done to make the expression easier to work with or to solve for a variable.

2. How do I expand a binomial expression?

To expand a binomial expression, use the FOIL method: multiply the First terms, then the Outer terms, then the Inner terms, and finally the Last terms. Simplify the resulting expression by combining like terms.

3. Can you give an example of simplifying an algebraic expression?

Sure, let's simplify the expression 3x + 6x - 2x. First, combine like terms to get 7x - 2x, which simplifies to 5x. So the simplified expression is 5x.

4. Why is it important to simplify algebraic expressions?

Simplifying algebraic expressions helps make them easier to understand and work with. It also allows us to see patterns and make connections between different expressions, making it easier to solve equations and manipulate them in various ways.

5. How can I check if my simplified expression is equivalent to the original one?

To check if two expressions are equivalent, substitute in a few values for the variables and see if the resulting values are the same for both expressions. You can also use algebraic techniques, such as factoring, to see if the two expressions can be written in the same form.

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