2-answer.jpeg "(2x+3y+4z)2 Answer")
Expansion of (2x+3y+4z)²
In algebra, expanding an expression involves removing the parentheses by multiplying the terms inside the parentheses with the terms outside. When we are dealing with a binomial expression like (2x+3y+4z)², we need to follow the rules of exponents and the distributive property of multiplication over addition.
Step 1: Multiply the expression by itself
(2x+3y+4z)² = (2x+3y+4z) × (2x+3y+4z)
Step 2: Multiply each term in the first expression with each term in the second expression
= 2x × 2x + 2x × 3y + 2x × 4z + 3y × 2x + 3y × 3y + 3y × 4z + 4z × 2x + 4z × 3y + 4z × 4z
Step 3: Simplify the expression
= 4x² + 6xy + 8xz + 6xy + 9y² + 12yz + 8xz + 12yz + 16z²
Step 4: Combine like terms
= 4x² + 12xy + 16xz + 9y² + 24yz + 16z²
Therefore, the expansion of (2x+3y+4z)² is:
(2x+3y+4z)² = 4x² + 12xy + 16xz + 9y² + 24yz + 16z²
This expansion is useful in various mathematical applications, such as algebraic manipulations, equation solving, and calculus.
