Understanding Notable Products in Algebra

The video tutorial covers the concept of notable products in algebra, focusing on the binomial square and binomial cube. It explains the formulas and provides examples to illustrate how these algebraic expressions are developed and applied. The tutorial also includes exercises to reinforce understanding and application of these concepts.

What is a notable product in algebra?

• A result obtained through many operations

• A result obtained through subtraction

• A result obtained through few operations

• A result obtained through addition

Which of the following is the first notable product discussed?

• Sum of two binomials

• Binomial square

• Product of two binomials

• Binomial cube

How is the binomial square (a + b)^2 developed?

• a^2 + 2ab + b^2

• a^2 + b^2

• a^2 + ab + b^2

• a^2 - 2ab + b^2

What is the result of (3x - 4)^2?

• 9x^2 - 24x - 16

• 9x^2 - 12x + 16

• 9x^2 + 24x + 16

• 9x^2 - 24x + 16

What is the correct development of (9x + 2)^2?

• 81x^2 + 18x + 4

• 81x^2 + 36x + 2

• 81x^2 + 18x + 2

• 81x^2 + 36x + 4

What is the form of a binomial cube?

• (a + b)^3

• (a - b)^2

• (a + b)^2

• (a - b)^3

How is the binomial cube (a + b)^3 developed?

• a^3 - 2a^2b + 2ab^2 - b^3

• a^3 + 2a^2b + 2ab^2 + b^3

• a^3 + 3a^2b + 3ab^2 + b^3

• a^3 - 3a^2b + 3ab^2 - b^3

What is the result of (2x + 3)^3?

• 8x^3 + 12x^2 + 18x + 27

• 8x^3 + 36x^2 + 54x + 27

• 8x^3 + 24x^2 + 36x + 27

• 8x^3 + 18x^2 + 27x + 27

What is the correct development of (5x - 1)^3?

• 125x^3 - 50x^2 + 25x - 1

• 125x^3 - 75x^2 + 25x - 1

• 125x^3 - 75x^2 + 15x - 1

• 125x^3 - 50x^2 + 15x - 1

What is the result of (4x + 7)^2?

• 16x^2 + 56x + 14

• 16x^2 + 56x + 49

• 16x^2 + 28x + 14

• 16x^2 + 28x + 49