Calculate Rectangle Area with Dimensions 2x and (2x-8): Variable Expression Problem

Q: Why do I need to use the distributive property here?

When multiplying $ 2x $ by $ (2x-8) $, you must distribute the $ 2x $ to both terms inside the parentheses. This gives you $ 2x \times 2x - 2x \times 8 $.

Q: What's the difference between area and perimeter?

Area measures the space inside the rectangle (length × width), while perimeter measures the distance around the rectangle (2 × length + 2 × width). Don't confuse them!

Q: How do I multiply 2x times 2x?

When multiplying variables with the same base, add the exponents: $ 2x \times 2x = 2 \times 2 \times x \times x = 4x^2 $.

Q: Can I simplify the final answer further?

The answer $ 4x^2 - 16x $ can be factored as $ 4x(x - 4) $, but both forms are correct. The expanded form is usually preferred for area problems.

Q: What if x has a specific value?

If given a specific value for x, substitute it into $ 4x^2 - 16x $ to find the numerical area. But since no value is given, leave your answer in variable form.

Rectangle Area with Variable Expressions

The width of a rectangle is equal to $2x$ cm and its length is $2x-8$ cm.

Calculate the area of the rectangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the area of the rectangle

00:03 Apply the formula for calculating the area of a rectangle (side x side)

00:09 Substitute the relevant values into the formula according to the given data and proceed to solve for the area

00:13 Expand the brackets properly - multiply each factor

00:26 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The width of a rectangle is equal to $2x$ cm and its length is $2x-8$ cm.

Calculate the area of the rectangle.

Step-by-step solution

The area of a rectangle is equal to length multiplied by width

Let's input the known data into the formula:

$S=2x\times(2x-8)$

$S=2x\times2x-2x\times8$

$S=4x^2-16x$

Final Answer

$4X^2-16X$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of rectangle equals length times width
Technique: Use distributive property: 2x(2x-8) = 4x² - 16x
Check: Expand step-by-step and combine like terms correctly ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't calculate 2x + (2x-8) = 4x-8! This gives the perimeter, not area. Area requires multiplication of dimensions. Always multiply length × width for rectangle area.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

Why do I need to use the distributive property here?

When multiplying $2x$ by $(2x-8)$ , you must distribute the $2x$ to both terms inside the parentheses. This gives you $2x \times 2x - 2x \times 8$ .

What's the difference between area and perimeter?

Area measures the space inside the rectangle (length × width), while perimeter measures the distance around the rectangle (2 × length + 2 × width). Don't confuse them!

How do I multiply 2x times 2x?

When multiplying variables with the same base, add the exponents: $2x \times 2x = 2 \times 2 \times x \times x = 4x^2$ .

Can I simplify the final answer further?

The answer $4x^2 - 16x$ can be factored as $4x(x - 4)$ , but both forms are correct. The expanded form is usually preferred for area problems.

What if x has a specific value?

If given a specific value for x, substitute it into $4x^2 - 16x$ to find the numerical area. But since no value is given, leave your answer in variable form.

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