How do you simplify $(x - 4)(x + 8)$ ?

Hint: In this question, we are given two algebraic expressions in terms of one variable in two brackets and they are in multiplication with each other, and we have to simplify them, that is, we have to multiply them to express them most easily and understandably. To multiply these two terms we will multiply the first term in the first bracket with the whole second bracket and then we will multiply the second term of the first bracket with the whole second bracket and then we will perform the given arithmetic operations like addition, subtraction, division and multiplication to get the simplified form of the given expression.

Complete step-by-step solution:
We have to simplify $(x - 4)(x + 8)$ , it is done as –
$
  (x - 4)(x + 8) = x(x + 8) - 4(x + 8) \\
   \Rightarrow (x - 4)(x + 8) = {x^2} + 8x - 4x - 32 \\
   \Rightarrow (x - 4)(x + 8) = {x^2} + 4x - 32 \\
 $
Hence, the simplified form of $(x - 4)(x + 8)$is ${x^2} + 4x - 32$ .

Note: The operation performed in the above solution is known as distributive property. All the numbers and algebraic expressions have certain properties, so we have generalized most of them for making the calculations easier. The three properties namely, commutative, associative and distributive property are widely used. The distributive property helps to make the multiplications a lot easier, so it is also called the distributive law of multiplication. According to this property, the product of a number (a) with a sum or difference of other two numbers is equal to the sum of the product of the number (a) with first number (b) and the product of the number (a) with the second number (c), that is, \[a(b + c) = ab + ac\].