-(9x2-%2B-4y2-%2B-4z2-%E2%80%93-6xy-%E2%80%93-4yz-%E2%80%93-6zx).jpeg "(3x + 2y + 2z) (9x2 + 4y2 + 4z2 – 6xy – 4yz – 6zx)")
Expanding and Simplifying Algebraic Expressions
In this article, we will explore the expansion and simplification of an algebraic expression involving three variables: x, y, and z. The expression in question is:
(3x + 2y + 2z) (9x² + 4y² + 4z² – 6xy – 4yz – 6zx)
Step 1: Expand the Expression
To expand the expression, we will multiply each term in the first bracket with each term in the second bracket.
(3x + 2y + 2z) (9x²) = 27x³ + 18xy + 18xz (3x + 2y + 2z) (4y²) = 12xy² + 8y³ + 8yz² (3x + 2y + 2z) (4z²) = 12xz² + 8y²z + 8z³ (3x + 2y + 2z) (-6xy) = -18x²y - 12xy² - 12xyz (3x + 2y + 2z) (-4yz) = -12xyz - 8y²z - 8yz² (3x + 2y + 2z) (-6zx) = -18x²z - 12xyz - 12xz²
Step 2: Combine Like Terms
Now, let's combine like terms:
- x³ term: 27x³
- xy term: 18xy - 18x²y - 12xy² = -18x²y - 6xy²
- xz term: 18xz - 18x²z - 12xyz = -18x²z - 6xyz
- y² term: 12xy² + 8y³ = 8y³ + 12xy²
- yz term: 8yz² - 12xyz - 8y²z = -4y²z - 4xyz
- z² term: 12xz² + 8z³ = 8z³ + 12xz²
- y³ term: 8y³
- z³ term: 8z³
Simplified Expression
The final simplified expression is:
27x³ - 18x²y - 6xy² - 18x²z - 6xyz + 8y³ - 4y²z - 4xyz + 8z³ + 12xz²
This is the expanded and simplified form of the original expression.
