Draw a diagram to represent the identity (a + b)2 = a2 + 2ab + b2.

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Sure! Here's a step-by-step diagram to represent the identity (a + b)² = a² + 2ab + b².

Step 1: Start with the expression (a + b)².

(a + b)²

Step 2: Expand the expression using the distributive property. Multiply each term in the first bracket by each term in the second bracket.

(a + b)(a + b)

Step 3: Apply the distributive property to simplify the expression.

a(a + b) + b(a + b)

Step 4: Multiply each term inside the brackets by the corresponding terms outside the brackets.

a² + ab + ab + b²

Step 5: Combine like terms.

a² + 2ab + b²

And there you have it! The diagram represents the identity (a + b)² = a² + 2ab + b².

To draw a diagram representing the identity (a + b)2 = a2 + 2ab + b2, we can use a visual method known as an area model.

First, draw a square with side length a + b. Label the sides as a + b.

[Diagram: Square with side length a + b labeled]

Next, divide the square into four smaller rectangles. The two rectangles at the top and bottom should have side lengths a, and the two rectangles at the sides should have side lengths b.

[Diagram: Square divided into four rectangles]

Now, label the sides of each rectangle. The top rectangle should have sides labeled as a, the bottom rectangle should also have sides labeled as a, the left rectangle should have sides labeled as b, and the right rectangle should also have sides labeled as b.

[Diagram: Each rectangle labeled with respective side lengths]

To represent the equation (a + b)2 = a2 + 2ab + b2 visually, calculate the area of each of the rectangles:

- The area of the top rectangle is a * a = a2
- The area of the bottom rectangle is also a * a = a2
- The area of the left rectangle is b * b = b2
- The area of the right rectangle is also b * b = b2

Finally, add up the areas of all the rectangles to get the total area of the big square. It should be equal to the right side of the equation.

- The area of the top rectangle + the area of the bottom rectangle = a2 + a2 = 2a2
- The area of the right rectangle + the area of the left rectangle = b2 + b2 = 2b2
- The area of the four smaller rectangles together = 2a2 + 2b2

So, the total area of the big square (a + b)2 is equal to the sum of the areas of the four smaller rectangles, which is a2 + 2ab + b2.

[Diagram: Final representation of (a + b)2 = a2 + 2ab + b2 using the area model]

http://pespmc1.vub.ac.be/POS/turchFigs/IMG.FIG11.1.GIF