Understanding the Pyramid Structure

Oct 13, 2025 by leolavanderia.com.br 48 views

Introduction

In this pyramid puzzle, we are presented with a mathematical expression where the top brick is found by adding together the expressions in the two bricks below it. Our task is to determine the expression that should replace the question mark. To solve this puzzle, we will need to apply basic algebraic operations and simplify the resulting expression.

Understanding the Pyramid Structure

The pyramid structure consists of three bricks, each containing a mathematical expression. The top brick is represented by the question mark, and the two bricks below it are given as 5x² + 6x and 2x² + 4x. We are told that the top brick is found by adding together the expressions in the two bricks below it.

Breaking Down the Problem

To solve this puzzle, we need to add the expressions in the two bricks below the top brick. This can be represented as:

(5x² + 6x) + (2x² + 4x)

Simplifying the Expression

To simplify the expression, we need to combine like terms. Like terms are terms that have the same variable raised to the same power. In this case, we have two like terms: 5x² and 2x², and two like terms: 6x and 4x.

Combining Like Terms

We can combine the like terms by adding their coefficients. The coefficient of a term is the number that is multiplied by the variable. In this case, the coefficient of 5x² is 5, and the coefficient of 2x² is 2. Similarly, the coefficient of 6x is 6, and the coefficient of 4x is 4.

Simplifying the Expression

Using the distributive property, we can rewrite the expression as:

(5x² + 2x²) + (6x + 4x)

Combining Like Terms

Now, we can combine the like terms by adding their coefficients:

7x² + 10x

Simplifying the Expression

Therefore, the expression that should replace the question mark is 7x² + 10x.

Conclusion

In this pyramid puzzle, we were presented with a mathematical expression where the top brick is found by adding together the expressions in the two bricks below it. By applying basic algebraic operations and simplifying the resulting expression, we were able to determine the expression that should replace the question mark. The final answer is 7x² + 10x.

Additional Tips and Tricks

When simplifying expressions, it's essential to combine like terms by adding their coefficients.
The distributive property can be used to rewrite expressions and make them easier to simplify.
Algebraic operations, such as addition and multiplication, can be used to solve mathematical expressions.

Final Answer

Q: What is the pyramid puzzle?

A: The pyramid puzzle is a mathematical puzzle where the top brick is found by adding together the expressions in the two bricks below it.

Q: How do I solve the pyramid puzzle?

A: To solve the pyramid puzzle, you need to apply basic algebraic operations and simplify the resulting expression. You can start by adding the expressions in the two bricks below the top brick and then combine like terms.

Q: What are like terms?

A: Like terms are terms that have the same variable raised to the same power. For example, 5x² and 2x² are like terms because they both have the variable x raised to the power of 2.

Q: How do I combine like terms?

A: To combine like terms, you need to add their coefficients. The coefficient of a term is the number that is multiplied by the variable. For example, the coefficient of 5x² is 5, and the coefficient of 2x² is 2. You can combine these like terms by adding their coefficients: 5x² + 2x² = 7x².

Q: What is the distributive property?

A: The distributive property is a mathematical property that allows you to rewrite an expression by multiplying each term inside the parentheses by the factor outside the parentheses. For example, 2(x + 3) = 2x + 6.

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms and apply the distributive property. You can also use other algebraic operations, such as addition and multiplication, to simplify the expression.

Q: What are some common algebraic operations?

A: Some common algebraic operations include addition, subtraction, multiplication, and division. You can also use exponentiation, such as squaring or cubing, to simplify expressions.

Q: How do I apply algebraic operations to simplify expressions?

A: To apply algebraic operations to simplify expressions, you need to follow the order of operations (PEMDAS):

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate any multiplication and division operations from left to right.
Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What are some tips for simplifying expressions?

A: Some tips for simplifying expressions include:

Combining like terms
Applying the distributive property
Using algebraic operations, such as addition and multiplication
Following the order of operations (PEMDAS)

Q: How do I check my work when simplifying expressions?

A: To check your work when simplifying expressions, you can:

Plug in values for the variables to see if the expression simplifies correctly
Use a calculator to evaluate the expression
Check your work by re-reading the problem and making sure you followed the correct steps

Q: What are some common mistakes to avoid when simplifying expressions?

A: Some common mistakes to avoid when simplifying expressions include:

Forgetting to combine like terms
Not applying the distributive property
Not following the order of operations (PEMDAS)
Making errors when evaluating expressions inside parentheses