Understanding (a + b)² and (a - b)²

Understanding (a + b)² and (a - b)²

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains and proves the algebraic identities (a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b² using geometric methods. It starts by constructing squares and rectangles to visually demonstrate the identities. The tutorial divides the squares into parts to show how the identities are derived, providing a clear understanding of the algebraic expressions through geometric representation.

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18 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the expanded form of (a + b)²?

a² + b²

a² + 2ab + b²

a² - 2ab + b²

a² + ab + b²

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in proving the identity (a + b)²?

Construct a triangle with side a

Construct a rectangle with side b

Construct a square with side a

Construct a square with side (a + b)

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How many distinct parts is the square divided into to prove (a + b)²?

Five

Four

Three

Two

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the area of the square with side a?

ab

2ab

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the area of the rectangle with sides a and b?

2ab

ab

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of dividing the square into parts in the (a + b)² proof?

To find the perimeter

To find the diagonal

To find the volume

To find the area

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the relationship between the areas of the parts and the whole square in the (a + b)² proof?

The parts are larger

The parts are smaller

The parts sum up to the whole

The parts are equal to the whole

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