Subjects algebra

Arithmetic Rewriting

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Arithmetic Rewriting


1. The phrase "normal arithmetic expressions" typically means writing mathematical expressions using standard arithmetic operators such as addition (+), subtraction (-), multiplication (×), division (÷), and exponentiation. 2. Without a specific expression given, I will explain a general example: rewriting an algebraic expression like $2(x+3)^2 - 5$ in normal arithmetic form. 3. Start by expanding the square using the formula $(a+b)^2 = a^2 + 2ab + b^2$: $$ (x+3)^2 = x^2 + 2\times x \times 3 + 3^2 = x^2 + 6x + 9 $$ 4. Substitute back into the expression: $$ 2(x^2 + 6x + 9) - 5 $$ 5. Distribute the 2: $$ 2 \times x^2 + 2 \times 6x + 2 \times 9 - 5 = 2x^2 + 12x + 18 - 5 $$ 6. Combine like terms: $$ 2x^2 + 12x + (18 - 5) = 2x^2 + 12x + 13 $$ 7. The expression rewritten in normal arithmetic form is: $$ 2x^2 + 12x + 13 $$ This illustrates rewriting algebraic terms using explicit arithmetic operations.