Quiz – \((a−b)^2\) – Geometric Derivation

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) \(3\)

Question 6

Expand:

\((2x-3)^2\)

A) \(4x^2-6x+9\)

B) \(4x^2-12x+9\)

C) \(2x^2-12x+9\)

Question 7

What is the middle term when expanding:

\((a-b)^2\)

A) \(-ab\)

B) \(-2ab\)

C) \(2ab\)

Question 8

Which term completes the expansion?

\((y-4)^2=y^2+\text{_____}+16\)

A) \(-4y\)

B) \(-8y\)

C) \(8y\)

Question 9

Which expression represents the geometric identity for the remaining square?

A) \(a^2-2ab+b^2\)

B) \(a^2-ab-b^2\)

C) \(a^2+2ab+b^2\)

Question 10

Evaluate using the identity:

\((8-3)^2\)

A) \(64-24+9=49\)

B) \(64-48+9=25\)

C) \(64-48-9=7\)

Answers

B) \((a−b)^2=a^2−2ab+b^2\)
B) \(x^2−4x+4\)
C) \(36\)
C) \((a−b)^2\)
B) \(2\)
B) \(4x^2-12x+9\)
B) \(-2ab\)
B) \(-8y\)
A) \(a^2-2ab+b^2\)
B) \(64-48+9=25\)

Mulkek