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Evaluating 4x22xy+3y24x^2 - 2xy + 3y^2 when x=2x = 2 and y=1y = -1

To evaluate a variable expression involving negative numbers and multiple variables, substitute the given values, using parentheses to preserve the operations and signs, and simplify using the order of operations.

For example, to evaluate 4x22xy+3y24x^2 - 2xy + 3y^2 when x=2x = 2 and y=1y = -1:

  1. Substitute: Replace xx with 22 and yy with 1-1. Use parentheses to clearly indicate multiplication and negative bases: 4(2)22(2)(1)+3(1)24(2)^2 - 2(2)(-1) + 3(-1)^2.
  2. Simplify exponents: Evaluate (2)2=4(2)^2 = 4 and (1)2=1(-1)^2 = 1. The expression becomes 4(4)2(2)(1)+3(1)4(4) - 2(2)(-1) + 3(1).
  3. Multiply: Perform all multiplications from left to right: 4(4)=164(4) = 16, 2(2)(1)=42(2)(-1) = -4, and 3(1)=33(1) = 3. The expression becomes 16(4)+316 - (-4) + 3.
  4. Subtract: The subtraction 16(4)16 - (-4) becomes 16+4=2016 + 4 = 20. The expression becomes 20+320 + 3.
  5. Add: 20+3=2320 + 3 = 23.

The final evaluated result is 2323.

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Updated 2026-05-01

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