Area of Square: Calculate Using Expression 4X+4Y

Q: Why do I need parentheses when squaring 4x+4y?

Parentheses are essential because you're squaring the entire expression, not just individual terms. Without parentheses, $ 4x+4y^2 $ means only the y is squared!

Q: Can I expand (4x+4y)² to get the final answer?

You could expand it to $ 16x^2 + 32xy + 16y^2 $, but (4x+4y)² is the most direct and correct form for representing the area.

Q: What if the side length was just a number, like 5?

The same rule applies! If the side is 5, the area is $ 5^2 = 25 $. For algebraic expressions, it's $ (expression)^2 $.

Q: Why isn't the answer just 4x+4y?

That's the perimeter of one side, not the area! Remember: area is always length × width, and for squares that means side × side = side².

Square Area with Algebraic Side Length

Look at the following square:

Which expression represents its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's start by expressing the area of the square.

00:07 We'll find the side length based on the given data.

00:11 Remember, the formula for the area of a square is the side length squared.

00:20 Now, plug in the values we have, and solve for the area.

00:35 Great job! That's how we find the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following square:

Which expression represents its area?

Step-by-step solution

The area of a square is equal to the measurement of one of its sides squared.

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=(4x+4y)^2$

Final Answer

$(4y+4x)^2$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared
Technique: Substitute given side (4x+4y) into $A = s^2$
Check: Final expression should be $(4x+4y)^2$ with parentheses ✓

Common Mistakes

Avoid these frequent errors

Forgetting to square the entire expression
Don't just multiply 4x+4y by 4 or square individual terms = wrong area formula! This gives 4(4x+4y) or 16x²+16y² instead of the correct squared expression. Always put the entire side length in parentheses and square it: (4x+4y)².

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square equivalent to?

FAQ

Everything you need to know about this question

Why do I need parentheses when squaring 4x+4y?

Parentheses are essential because you're squaring the entire expression, not just individual terms. Without parentheses, $4x+4y^2$ means only the y is squared!

Can I expand (4x+4y)² to get the final answer?

You could expand it to $16x^2 + 32xy + 16y^2$ , but (4x+4y)² is the most direct and correct form for representing the area.

What if the side length was just a number, like 5?

The same rule applies! If the side is 5, the area is $5^2 = 25$ . For algebraic expressions, it's $(expression)^2$ .

How do I know this is definitely a square and not a rectangle?

The problem states it's a square, and all sides of a square are equal in length. That's why we can use the single expression 4x+4y for the side length.

Why isn't the answer just 4x+4y?

That's the perimeter of one side, not the area! Remember: area is always length × width, and for squares that means side × side = side².

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