Test your understanding of the geometric derivation of:

\((a−b)^2=a^2−2ab+b^2\)

Try to answer the questions before checking the answers at the bottom of the page.

Question 1

Which identity is correct?

A) \((a−b)^2=a^2+b^2\)

B) \((a−b)^2=a^2−2ab+b^2\)

C) \((a−b)^2=a^2−2b^2\)

Question 2

Expand:

\((x−2)^2\)

A) \(x^2−2x+4\)

B) \(x^2−4x+4\)

C) \(x^2+4x+4\)

Question 3

Evaluate:

\((9−3)^2\)

A) \(18\)

B) \(24\)

C) \(36\)

Question 4

What is the area of a square with side:

\(a−b\)

A) \(a−b\)

B) \(2(a−b)\)

C) \((a−b)^2\)

Question 5

How many rectangles are removed in the geometric derivation?

A) \(1\)

B) \(2\)

C) \(3\)

Answers

1. B) \((a−b)^2=a^2−2ab+b^2\)
2. B) \(x^2−4x+4\)
3. C) \(36\)
4. C) \((a−b)^2\)
5. B) \(2\)

Practice

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Continue Learning

1. \((a – b)^2\) – Geometric Derivation
2. \((a + b)^2\) – Geometric Derivation
3. \(a^2 – b^2\) – Geometric Derivation
4. \(a^2 – b^2\) – Algebraic Proof

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