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) $(a+b)^2=a^2+ab+b^2$

Question 2

Expand:

$(x+3)^2$

A) $x^2+3x+9$

B) $x^2+6x+9$

C) $x^2+9x+9$

Question 3

Evaluate:

$(4+5)^2$

A) $81$

B) $64$

C) $49$

Question 4

What is the area of a square with side:

$a+b$

A) $a+b$

B) $(a+b)^2$

C) $2(a+b)$

Question 5

How many rectangles with area $ab$ ab appear 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) $a+b$

Question 8

Complete the expansion:

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

A) $4y$

B) $8y$

C) $16y$

Question 9

A square has side length $a+b$. It is divided into regions with areas:

$a^2,\ ab,\ ab,\ b^2$

What is the total area?

A) $a^2+ab+b^2$

B) $a^2+2ab+b^2$

C) $2a^2+2b^2$

Question 10

Evaluate using the identity:

$(7+2)^2$

A) $49+14+4=67$

B) $49+28+4=81$

C) $49+28+2=79$

Answers

B) $(a+b)^2=a^2+2ab+b^2$
B) $x^2+6x+9$
A) $81$
B) $(a+b)^2$
B) $2$
B) $4x^2+12x+9$
B) $2ab$
B) $8y$
B) $a^2+2ab+b^2$
B) $49+28+4=81$

Mulkek