Write the following expressions as simply as as possible

Write the following expressions as simply as as possible:
a) 2t × 9u
b) 7 x g x h x 3

The Correct Answer and Explanation is :

To simplify the given expressions, we will apply the basic rules of multiplication and the properties of numbers. Let’s break down each expression step by step.

a) Simplifying (2t \times 9u)

1. Identify Coefficients and Variables: In the expression (2t \times 9u), the coefficients are 2 and 9, while the variables are (t) and (u).
2. Multiply the Coefficients:
   [
   2 \times 9 = 18
   ]
3. Combine the Variables: Since multiplication is commutative, we can write:
   [
   t \times u = tu
   ]
4. Combine the Results: Putting it all together, we have:
   [
   2t \times 9u = 18tu
   ]

b) Simplifying (7 \times g \times h \times 3)

1. Identify Coefficients and Variables: In this expression, the coefficients are 7 and 3, while the variables are (g) and (h).
2. Multiply the Coefficients:
   [
   7 \times 3 = 21
   ]
3. Combine the Variables: The variables can be multiplied together:
   [
   g \times h = gh
   ]
4. Combine the Results: So, we can write:
   [
   7 \times g \times h \times 3 = 21gh
   ]

Summary of Results

• For part (a), the simplified expression is:
  [
  2t \times 9u = 18tu
  ]
• For part (b), the simplified expression is:
  [
  7 \times g \times h \times 3 = 21gh
  ]

Explanation

In both cases, we utilized the distributive property of multiplication, which states that when multiplying numbers or variables, we can rearrange and group them without changing the result. The simplification involved multiplying the numerical coefficients first and then combining the variables.

This approach not only streamlines expressions for easier handling in algebra but also helps when solving equations or performing further operations, as simpler forms are generally easier to manage. Understanding these basic principles is fundamental in algebra, enabling one to approach more complex problems with confidence.