Calculate Rectangle Area: Finding x(x-4) with Variable Dimensions

Q: Why can't I just add x and (x-4) to get the area?

Adding gives you perimeter information, not area! Area measures the space inside the rectangle, which requires multiplying the two dimensions together.

Q: How do I multiply x times (x-4)?

Use the distributive property: multiply x by each term inside the parentheses. So $ x \times (x-4) = x \times x + x \times (-4) = x^2 - 4x $

Q: Can I check my answer by plugging in a number for x?

Absolutely! Try $ x = 6 $: width = 6, length = 6-4 = 2, so area = 6×2 = 12. Using our formula: $ 6^2 - 4(6) = 36 - 24 = 12 $ ✓

Q: Why is the answer x²-4x and not 4x²?

Because we're multiplying x by (x-4), not 4x by x! The coefficient of x² comes from $ x \times x = x^2 $, which gives us 1, not 4.

Polynomial Multiplication with Variable Expressions

The width of a rectangle is equal to $x$ cm and its length is $x-4$ 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)

00:08 Substitute in the relevant values according to the given data and proceed to solve for the area

00:11 Expand the parentheses - multiply each factor

00:14 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 $x$ cm and its length is $x-4$ cm.

Calculate the area of the rectangle.

Step-by-step solution

The area of the rectangle is equal to the length times the width:

$S=x\times(x-4)$

$S=x^2-4x$

Final Answer

$X^2-4X$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Rectangle area equals length times width
Technique: Multiply x by (x-4) using distributive property: x(x-4) = x²-4x
Check: Verify by substituting test values like x=5: 5(5-4)=5×1=5, and 5²-4(5)=25-20=5 ✓

Common Mistakes

Avoid these frequent errors

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

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why can't I just add x and (x-4) to get the area?

Adding gives you perimeter information, not area! Area measures the space inside the rectangle, which requires multiplying the two dimensions together.

How do I multiply x times (x-4)?

Use the distributive property: multiply x by each term inside the parentheses. So $x \times (x-4) = x \times x + x \times (-4) = x^2 - 4x$

What if x is less than 4? Won't the length be negative?

Great observation! In real rectangles, all dimensions must be positive. So we need $x > 4$ for this to represent an actual rectangle.

Can I check my answer by plugging in a number for x?

Absolutely! Try $x = 6$ : width = 6, length = 6-4 = 2, so area = 6×2 = 12. Using our formula: $6^2 - 4(6) = 36 - 24 = 12$ ✓

Why is the answer x²-4x and not 4x²?

Because we're multiplying x by (x-4), not 4x by x! The coefficient of x² comes from $x \times x = x^2$ , which gives us 1, not 4.

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