Perfect Square Trinomials and Expansion

The video tutorial explains perfect square trinomials, which are formed by squaring a binomial. It covers how to expand and factor these trinomials using specific formulas. The tutorial provides examples of expanding binomials like (y-4)^2 and (x+10)^2, and factoring expressions such as z^2 + 6z + 9. The process involves identifying the square roots of the first and third terms and checking if the middle term matches the formula 2ab. The video emphasizes recognizing perfect square trinomials to simplify expansion and factoring.

What is a perfect square trinomial?

• A trinomial that can be factored into two identical binomials.

• A trinomial with three different terms.

• A trinomial with only one variable.

• A trinomial that cannot be factored.

Which of the following is the expanded form of (a + b)^2?

• a^2 + ab + b^2

• a^2 - 2ab + b^2

• a^2 + 2ab + b^2

• a^2 + b^2

When expanding (x + 10)^2, what is the middle term?

• 10x

• 40x

• 20x

• 30x

What is the result of expanding (y - 4)^2?

• y^2 - 16y + 16

• y^2 - 8y + 8

• y^2 - 8y + 16

• y^2 - 4y + 16

How do you determine if a trinomial is a perfect square?

• Check if the first and last terms are perfect squares and the middle term is twice the product of their roots.

• Check if all terms are perfect squares.

• Check if the trinomial can be divided by 2.

• Check if the trinomial has three terms.

What is the factored form of z^2 + 6z + 9?

• (z - 6)^2

• (z + 6)^2

• (z - 3)^2

• (z + 3)^2

In the expression 4q^2 - 40q + 25, what is the value of 'b' in the binomial (a - b)^2?

• 25

• 10

• 5

• 4

What is the expanded form of (3x - 2)^2?

• 9x^2 - 12x + 4

• 9x^2 - 12x - 4

• 9x^2 + 12x + 4

• 9x^2 - 6x + 4

Which of the following is NOT a characteristic of a perfect square trinomial?

• The middle term is twice the product of the roots of the first and last terms.

• The first and last terms are perfect squares.

• The trinomial can be expressed as the square of a binomial.

• The trinomial can be factored into two different binomials.

What is the first step in working with perfect square trinomials?

• Multiply the trinomial by itself.

• Factor the trinomial.

• Expand the trinomial.

• Determine if it is a perfect square.