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.