The product of the square of h and eight
The Correct Answer and Explanation is:
Correct Answer:
The product of the square of h and eight is: 8h28h^2
Explanation:
To understand the expression “the product of the square of h and eight,” we need to break down the mathematical terminology step by step.
- “Square of h” means multiplying h by itself. In algebraic notation, this is written as: h2h^2 This represents h × h.
- “Product” means the result of multiplication. So, when we are asked for the product of the square of h and eight, it means we are multiplying h² by 8.
- In mathematical terms, this is: 8×h28 × h^2 or more commonly written as: 8h28h^2
This is a monomial expression, where:
- 8 is the coefficient (the constant number),
- h is the variable,
- and ² (squared) indicates the variable is raised to the power of two.
Why It Matters:
Understanding expressions like 8h² is important in algebra, as they form the basis for more complex equations used in science, engineering, and everyday problem-solving. For example, if h represents height, h² could represent the area of a square, and 8h² could represent eight times that area—perhaps for eight identical plots of land.
Common Mistakes:
Some might misinterpret the phrase and write (8h)², which is: (8h)2=64h2(8h)^2 = 64h^2
But this is incorrect because it squares both the 8 and the h. The original question only asks for the square of h, not the square of 8 times h.
Final Expression:
8h2\boxed{8h^2}
