Test your understanding of the geometric derivation of:
\(a^2−b^2=(a+b)(a−b)\)
Try to answer the questions before checking the answers at the bottom of the page.
Question 1
Which identity is correct?
A) \(a^2−b^2=(a−b)^2\)
B) \(a^2−b^2=(a+b)(a−b)\)
C) \(a^2−b^2=a+b\)
Question 2
Simplify:
\(x^2−9\)
A) \((x+9)(x−9)\)
B) \((x+3)(x−3)\)
C) \((x−3)^2\)
Question 3
Evaluate:
\(10^2−6^2\)
A) \(64\)
B) \(72\)
C) \(36\)
Question 4
What are the dimensions of the rectangle formed in the geometric derivation?
A) \(a\) and \(b\)
B) \(a+b\) and \(a−b\)
C) \(a^2\) and \(b^2\)
Question 5
Simplify:
\(y^2−49\)
A) \((y+7)(y−7)\)
B) \((y+49)(y−49)\)
C) \((y−7)^2\)
Question 6
Simplify:
\(4x^2-25\)
A) \((2x+5)(2x-5)\)
B) \((4x+5)(4x-5)\)
C) \((2x-5)^2\)
Question 7
Evaluate using the difference of two squares identity:
\(12^2-8^2\)
A) \(16\)
B) \(64\)
C) \(80\)
Question 8
A large square has side length \(9\), and a smaller square inside it has side length \(4\).
What is the remaining area?
A) \(77\)
B) \(65\)
C) \(25\)
Question 9
Which expression is not a difference of two squares?
A) \(x^2-36\)
B) \(25-y^2\)
C) \(x^2+16\)
Question 10
Simplify:
\(9a^2-b^2\)
A) \((3a+b)(3a-b)\)
B) \((9a+b)(9a-b)\)
C) \((3a-b)^2\)
Answers
- B) \(a^2−b^2=(a+b)(a−b)\)
- B) \((x+3)(x−3)\)
- A) \(64\)
- B) \(a+b\) and \(a−b\)
- A) \((y+7)(y−7)\)
- A) \((2x+5)(2x-5)\)
- C) \(80\)
- B) \(65\)
- C) \(x^2+16\)
- A) \((3a+b)(3a-b)\)
Practice
- Take the Quiz (Current page)
Continue Learning
- \((a – b)^2\) – Geometric Derivation
- \((a + b)^2\) – Geometric Derivation
- \(a^2 – b^2\) – Geometric Derivation
- \(a^2 – b^2\) – Algebraic Proof