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Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Draw a square axa a square bxb and, 2 rectangles axb on it. Cut off figures as shown *(Instructions needs to be given in class)?
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Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Dra...
Verification of (a b)2 = a2 b2 2ab
Materials needed:
- Piece of cardboard
- Ruler
- Pencil
- Scissors
Instructions:
1. Begin by drawing a square with sides of length 'a' and another square with sides of length 'b' on the cardboard.
2. Next, draw two rectangles with dimensions 'a' by 'b' on the cardboard.
3. Cut out the shapes carefully along the drawn lines.
4. Arrange the cut-out shapes to form a larger square with sides of length '(a+b)'.
5. Now, calculate the area of the larger square by multiplying '(a+b)' with itself, i.e., (a+b)^2.
6. Calculate the area of the smaller square with sides of length 'a' by multiplying 'a' with itself, i.e., a^2.
7. Calculate the area of the smaller square with sides of length 'b' by multiplying 'b' with itself, i.e., b^2.
8. Calculate the combined area of the two rectangles by multiplying 'a' and 'b' and then multiplying the result by 2, i.e., 2ab.
9. Compare the area of the larger square with the sum of the areas of the two smaller squares and the combined area of the rectangles.
10. You will observe that (a+b)^2 = a^2 + b^2 + 2ab, thus verifying the given identity.
This hands-on activity helps visually understand the algebraic concept of expanding a binomial squared and reinforces the relationship between the squares of binomials and the product of the sum and difference of the terms.
Materials needed:
- Piece of cardboard
- Ruler
- Pencil
- Scissors
Instructions:
1. Begin by drawing a square with sides of length 'a' and another square with sides of length 'b' on the cardboard.
2. Next, draw two rectangles with dimensions 'a' by 'b' on the cardboard.
3. Cut out the shapes carefully along the drawn lines.
4. Arrange the cut-out shapes to form a larger square with sides of length '(a+b)'.
5. Now, calculate the area of the larger square by multiplying '(a+b)' with itself, i.e., (a+b)^2.
6. Calculate the area of the smaller square with sides of length 'a' by multiplying 'a' with itself, i.e., a^2.
7. Calculate the area of the smaller square with sides of length 'b' by multiplying 'b' with itself, i.e., b^2.
8. Calculate the combined area of the two rectangles by multiplying 'a' and 'b' and then multiplying the result by 2, i.e., 2ab.
9. Compare the area of the larger square with the sum of the areas of the two smaller squares and the combined area of the rectangles.
10. You will observe that (a+b)^2 = a^2 + b^2 + 2ab, thus verifying the given identity.
This hands-on activity helps visually understand the algebraic concept of expanding a binomial squared and reinforces the relationship between the squares of binomials and the product of the sum and difference of the terms.
Community Answer
Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Dra...
Write five rational number which are smaller than 2
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Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Draw a square axa a square bxb and, 2 rectangles axb on it. Cut off figures as shown *(Instructions needs to be given in class)?
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Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Draw a square axa a square bxb and, 2 rectangles axb on it. Cut off figures as shown *(Instructions needs to be given in class)? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Draw a square axa a square bxb and, 2 rectangles axb on it. Cut off figures as shown *(Instructions needs to be given in class)? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Draw a square axa a square bxb and, 2 rectangles axb on it. Cut off figures as shown *(Instructions needs to be given in class)?.
Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Draw a square axa a square bxb and, 2 rectangles axb on it. Cut off figures as shown *(Instructions needs to be given in class)? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Draw a square axa a square bxb and, 2 rectangles axb on it. Cut off figures as shown *(Instructions needs to be given in class)? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Verification of (a b)2 = a2 b2 2ab Take a piece of card board. Draw a square axa a square bxb and, 2 rectangles axb on it. Cut off figures as shown *(Instructions needs to be given in class)?.
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