2-answer.jpeg "(2x+3y+4z)2 Answer")
Expanding the Square: (2x + 3y + 4z)²
Expanding the square of a trinomial like (2x + 3y + 4z)² can be achieved using the distributive property or FOIL method and a bit of pattern recognition.
Here's how to break down the expansion:
1. Recognizing the Pattern
We can see that (2x + 3y + 4z)² is essentially the same as (a + b + c)², where:
- a = 2x
- b = 3y
- c = 4z
2. Expanding Using Distributive Property
We can expand the expression by multiplying each term in the first trinomial by each term in the second trinomial:
(2x + 3y + 4z)² = (2x + 3y + 4z)(2x + 3y + 4z)
Now, we distribute each term:
= 2x(2x + 3y + 4z) + 3y(2x + 3y + 4z) + 4z(2x + 3y + 4z)
3. Simplifying
Finally, we multiply and combine like terms:
= 4x² + 6xy + 8xz + 6xy + 9y² + 12yz + 8xz + 12yz + 16z²
= 4x² + 9y² + 16z² + 12xy + 16xz + 24yz
Therefore, the expanded form of (2x + 3y + 4z)² is 4x² + 9y² + 16z² + 12xy + 16xz + 24yz.
Key Points:
- Pattern recognition helps to simplify the process.
- The distributive property is a fundamental algebraic concept.
- Combining like terms ensures a simplified expression.
Expanding trinomials can be challenging, but understanding the underlying principles and practicing will make it easier.