Final answer
This is obtained by applying the distributive property twice. First, we distribute the 4 to the terms inside the parentheses in the expression 4(5 + 2), which gives us 4x^7 = 4x^5 + 4x^2. Next, we simplify this expression by combining like terms, resulting in 20 (when x^5 is raised to the power of 1) and 8 (when x^2 is raised to the power of 1). Therefore, the final answer is 28 (which is the sum of these two terms).
Explaination:
In this problem, we used the distributive property, which is an axiom in algebra. This axiom allows us to distribute a common factor outside a set of parentheses to each term inside the parentheses. For example, in the expression 4(5 + 2), we can distribute the 4 to each term inside the parentheses as follows:
4(5 + 2) = 4 * 5 + 4 * 2
This results in the expression we used in our solution: 4x^7 = 4x^5 + 4x^2. The distributive property is a fundamental concept in algebra that helps us simplify expressions and solve equations. It allows us to break down complex expressions into simpler ones that are easier to work with. By applying this axiom, we were able to solve this problem and arrive at our final answer of 28.