The order of operations in algebra dictates the order in which arithmetic operations should be performed to ensure getting the correct answer for an equation. Deviation from the order of operations can result in incorrect arithmetic. Simplify expressions enclosed in parentheses first, then apply exponents. Multiply and divide terms that require it, and finally add and subtract.
For example, take the expression (3x + 5) - 2 * (4x)^2 + 15. To start, solve the (4x)^2 to 16x^2, and multiply it by 2, giving you 32x^2. The expression is now (3x + 5) - 32x^2 + 15. The expression has been simplified as far as it can be; expressions in parentheses like the 3x + 5 are considered single terms because they cannot be simplified without knowledge of the variable's quantity.
If the parenthetical expression had been (3 + 5) without the x, it could have been reduced to 8, but only like terms can be added or subtracted. Other terms are multiplied or divided. If a number is immediately outside parentheses, use the distributive property to multiply it by each of the grouped terms. For example, 4(3x + 2) comes to 12x + 8. When you factor equations, you have to break these terms apart, but for following the order of operations, have as few terms as possible.