Binomial Expansion and Patterns

Mrs. Yaod introduces Algebra 1 students to special products of polynomials, focusing on the square of a binomial and the sum and difference patterns. She explains shortcuts for these patterns and demonstrates them using the distributive and box methods. Students are encouraged to practice problems and understand the importance of standard form in polynomials.

What is the shortcut for finding the square of a binomial (a + b)^2?

• a^2 + 2ab + b^2

• a^2 - b^2

• a^2 - 2ab + b^2

• a^2 + b^2

In the distributive method, what is the result of multiplying (a + b)(a + b)?

• a^2 + 2ab + b^2

• a^2 + ab + b^2

• a^2 - 2ab + b^2

• a^2 + b^2

What is the result of using the box method for (a - b)^2?

• a^2 + 2ab + b^2

• a^2 - 2ab + b^2

• a^2 - b^2

• a^2 + b^2

What is the shortcut for the sum and difference pattern (a + b)(a - b)?

• a^2 - b^2

• a^2 + b^2

• a^2 - 2ab + b^2

• a^2 + 2ab + b^2

If x + 3 and x - 3 are multiplied, what is the result?

• x^2 + 9

• x^2 - 9

• x^2 - 6x + 9

• x^2 + 6x + 9

What is the expanded form of (a + 3)^2 using the shortcut?

• a^2 + 6a + 9

• a^2 + 9

• a^2 + 3a + 9

• a^2 + 6a

What is the result of (x - 2)^2 using the shortcut?

• x^2 - 4x + 4

• x^2 + 4x + 4

• x^2 + 4

• x^2 - 4

What is the result of (3x + 4)(3x - 4) using the sum and difference pattern?

• 9x^2 - 16

• 9x^2 - 24x + 16

• 9x^2 + 24x + 16

• 9x^2 + 16

What is the expanded form of (t + 11)(t - 11)?

• t^2 + 121

• t^2 - 121

• t^2 + 22t + 121

• t^2 - 22t + 121

What is the result of (1/2c + 1/3)(1/2c - 1/3) using the sum and difference pattern?

• 1/4c^2 - 2/3c + 1/9

• 1/4c^2 + 2/3c + 1/9

• 1/4c^2 - 1/9

• 1/4c^2 + 1/9