To expand algebraic expressions, we typically use the distributive property, also known as the distributive law. This property states that \( a(b + c) = ab + ac \). We can apply this property to expand expressions involving parentheses.
Example of Expanding
Let’s expand the expression:
\[ 3(x + 4) \]
Using the distributive property:
\[ 3(x + 4) = 3x + 3 \cdot 4 = 3x + 12 \]
More Complex Example
Expand the expression:
\[ 2(x + 3) + 4(2x - 1) \]
First, apply the distributive property to both terms:
- \( 2(x + 3) = 2x + 6 \)
- \( 4(2x - 1) = 8x - 4 \)
Now, combine these results:
\[ 2x + 6 + 8x - 4 = (2x + 8x) + (6 - 4) = 10x + 2 \]
Determine if Expressions are Equivalent
To determine if two expressions are equivalent, we can evaluate them at specific values of the variable or simplify both expressions to see if they match.
Example
Consider the expressions:
- \( 2(x + 3) \)
- \( 2x + 6 \)
Let’s evaluate both at \( x = 1 \):
For \( 2(x + 3) \):
\[ 2(1 + 3) = 2 \cdot 4 = 8 \]
For \( 2x + 6 \):
\[ 2 \cdot 1 + 6 = 2 + 6 = 8 \]
Since both expressions yield the same result when evaluated at \( x = 1 \), they are equivalent.
If you have specific algebraic expressions you'd like expanded or evaluated for equivalence, feel free to share!
1 answer