Area of Square with Side Length 5+2x: Express in Algebraic Form

Square Area with Algebraic Expressions

Look at the following square:

AAABBBDDDCCC5+2X

Express the area of the square in terms of x x .

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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 The side length according to the given data
00:07 We'll use the formula for calculating the area of a square (side squared)
00:13 We'll substitute appropriate values and solve to find the area
00:19 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following square:

AAABBBDDDCCC5+2X

Express the area of the square in terms of x x .

2

Step-by-step solution

Remember that the area of a square is equal to the side of the square squared.

The formula for the area of a square is:

S=a2 S=a^2

Finally, substitute the data into the formula:

S=(5+2x)2 S=(5+2x)^2

3

Final Answer

(5+2x)2 (5+2x)^2

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared
  • Technique: Square the entire expression: (5+2x)2 (5+2x)^2
  • Check: Verify all sides equal 5+2x and formula gives correct units ✓

Common Mistakes

Avoid these frequent errors
  • Only squaring part of the side length expression
    Don't square just the 5 or just the 2x = wrong area formula! This ignores that the entire expression (5+2x) is one complete side length. Always square the complete side length expression as one unit: (5+2x)2 (5+2x)^2 .

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

111111

What is the area of the square?

FAQ

Everything you need to know about this question

Why can't I just write 25 + 4x² as the area?

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Because that's only squaring the individual parts! When you square (5+2x)2 (5+2x)^2 , you need to use the perfect square formula: (a+b)2=a2+2ab+b2 (a+b)^2 = a^2 + 2ab + b^2 , which gives 25+20x+4x2 25 + 20x + 4x^2 .

How do I know the side length is 5+2x and not something else?

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Look at the diagram carefully! The side is labeled as 5+2X (which is the same as 5+2x). In a square, all four sides are equal, so each side has length 5+2x.

What if x has a specific value? Do I substitute first?

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No! The question asks for the area in terms of x, meaning keep x as a variable. Your final answer should be the algebraic expression (5+2x)2 (5+2x)^2 .

Should I expand (5+2x)² or leave it as is?

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The question asks to "express the area," so (5+2x)2 (5+2x)^2 is the correct form. Some teachers prefer this factored form, while others want it expanded. Check your specific instructions!

How is this different from finding the perimeter?

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Great question! Perimeter adds all four sides: 4(5+2x) = 20+8x. Area multiplies length × width: (5+2x) × (5+2x) = (5+2x)2 (5+2x)^2 . Don't mix them up!

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