Calculate Square Area: Side Length (8-3X) Problem

Q: Why is (-3x+8)² the same as (8-3x)²?

These expressions are equivalent because addition is commutative! The terms 8 and -3x can be written in any order: $ 8 + (-3x) = (-3x) + 8 $.

Q: Do I need to expand the squared expression?

Not necessarily! The question asks for the area, and $ (8-3x)^2 $ is a perfectly valid answer. Expanding would give you the standard form, but both are correct.

Q: What if the side length becomes negative?

In geometry problems, we assume the side length is positive. The expression 8-3x represents a length, so we consider values of x where 8-3x > 0.

Q: How do I know which answer choice matches my work?

Look for equivalent expressions! Since (8-3x)² = (-3x+8)², both represent the same area. Choose the form that matches one of the given options.

Square Area with Algebraic Side Length

Look at the following square:

What is its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the area of the square

00:03 Side length according to the given data

00:10 We'll use the formula for calculating square area (side squared)

00:19 We'll substitute appropriate values and solve to find the area

00:29 We'll reverse the writing order

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following square:

What is its area?

Step-by-step solution

The area of a square is equal to the side of the square raised to the 2nd power:

$S=a^2$

$S=(8-3x)^2$

$S=(-3x+8)^2$

Final Answer

$(-3x+8)^2$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of a square equals side length squared
Technique: Write (8-3x)² as (-3x+8)² using commutative property
Check: Both forms represent the same expression when squared ✓

Common Mistakes

Avoid these frequent errors

Squaring only part of the side length expression
Don't square just one term like (8)² or (-3x)² = wrong area! This ignores the algebraic expression as a complete unit. Always square the entire side length expression as one piece: (8-3x)².

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square?

FAQ

Everything you need to know about this question

Why is (-3x+8)² the same as (8-3x)²?

These expressions are equivalent because addition is commutative! The terms 8 and -3x can be written in any order: $8 + (-3x) = (-3x) + 8$ .

Do I need to expand the squared expression?

Not necessarily! The question asks for the area, and $(8-3x)^2$ is a perfectly valid answer. Expanding would give you the standard form, but both are correct.

What if the side length becomes negative?

In geometry problems, we assume the side length is positive. The expression 8-3x represents a length, so we consider values of x where 8-3x > 0.

How do I know which answer choice matches my work?

Look for equivalent expressions! Since (8-3x)² = (-3x+8)², both represent the same area. Choose the form that matches one of the given options.

Can I substitute a number for x to check my answer?

Yes! Pick a simple value like x = 1. Then (8-3(1))² = 5² = 25, and (-3(1)+8)² = 5² = 25. Same result confirms they're equivalent!

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