(x+2y+3z)2 Solution

Jasonbradley

2 min read

·

Jun 16, 2024

19

Share

Expanding (x + 2y + 3z)²

The expression (x + 2y + 3z)² represents the square of a trinomial. To solve it, we need to expand the expression using the distributive property or the binomial theorem.

Using the Distributive Property:

1. Rewrite the expression: (x + 2y + 3z)² = (x + 2y + 3z)(x + 2y + 3z)
2. Expand by multiplying each term in the first trinomial by each term in the second trinomial:
   • x(x + 2y + 3z) + 2y(x + 2y + 3z) + 3z(x + 2y + 3z)
3. Simplify by multiplying:
   • x² + 2xy + 3xz + 2xy + 4y² + 6yz + 3xz + 6yz + 9z²
4. Combine like terms:
   • x² + 4xy + 6xz + 4y² + 12yz + 9z²

Using the Binomial Theorem:

While the binomial theorem is typically used for expanding expressions with two terms, we can adapt it for this case.

1. Recognize the pattern: (a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc
2. Apply the pattern to our expression:
   • a = x, b = 2y, c = 3z
3. Substitute and simplify:
   • x² + (2y)² + (3z)² + 2(x)(2y) + 2(x)(3z) + 2(2y)(3z)
   • x² + 4y² + 9z² + 4xy + 6xz + 12yz

Therefore, the solution for (x + 2y + 3z)² is: x² + 4xy + 6xz + 4y² + 12yz + 9z²