Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

### Multiplying Monomials and Binomials

Identifying Special Products of Binomial Multiplication

Which products result in a difference of squares or a perfect square trinomial? Check all that apply.

- (5x + 3)(5x - 3)
- (7x + 4)(7x + 4)
- (2x + 1)(x + 2)
- (4x - 6)(x + 8)
- (x - 9)(x - 9)
- (-3x - 6)(-3x + 6)

Sagot :

GinnyAnswer
To identify which products result in a difference of squares or a perfect square trinomial, we need to know a few algebraic identities:

1. Difference of Squares:
[tex]\((a + b)(a - b) = a^2 - b^2\)[/tex]

2. Perfect Square Trinomial:
[tex]\((a + b)^2 = a^2 + 2ab + b^2\)[/tex] or [tex]\((a - b)^2 = a^2 - 2ab + b^2\)[/tex]

Let's analyze each product:

1. [tex]\((5x + 3)(5x - 3)\)[/tex]
- This follows the form of a difference of squares: [tex]\(a = 5x\)[/tex] and [tex]\(b = 3\)[/tex].
- [tex]\((5x + 3)(5x - 3) = (5x)^2 - 3^2 = 25x^2 - 9\)[/tex]
- This matches the difference of squares identity.

2. [tex]\((7x + 4)(7x + 4)\)[/tex]
- This follows the form of a perfect square trinomial: [tex]\(a = 7x\)[/tex] and [tex]\(b = 4\)[/tex].
- [tex]\((7x + 4)^2 = (7x)^2 + 2(7x)(4) + 4^2 = 49x^2 + 56x + 16\)[/tex]
- This matches the perfect square trinomial identity.

3. [tex]\((2x + 1)(x + 2)\)[/tex]
- This does not follow the form of either a difference of squares or a perfect square trinomial.
- Multiplying it out, [tex]\((2x + 1)(x + 2) = 2x^2 + 4x + x + 2 = 2x^2 + 5x + 2\)[/tex]
- This is neither a difference of squares nor a perfect square trinomial.

4. [tex]\((4x - 6)(x + 8)\)[/tex]
- This does not follow the form of either a difference of squares or a perfect square trinomial.
- Multiplying it out, [tex]\((4x - 6)(x + 8) = 4x^2 + 32x - 6x - 48 = 4x^2 + 26x - 48\)[/tex]
- This is neither a difference of squares nor a perfect square trinomial.

5. [tex]\((x - 9)(x - 9)\)[/tex]
- This follows the form of a perfect square trinomial: [tex]\(a = x\)[/tex] and [tex]\(b = 9\)[/tex].
- [tex]\((x - 9)^2 = x^2 - 2(x)(9) + 9^2 = x^2 - 18x + 81\)[/tex]
- This matches the perfect square trinomial identity.

6. [tex]\((-3x - 6)(-3x + 6)\)[/tex]
- This follows the form of a difference of squares: [tex]\(a = -3x\)[/tex] and [tex]\(b = 6\)[/tex].
- [tex]\((-3x - 6)(-3x + 6) = (-3x)^2 - 6^2 = 9x^2 - 36\)[/tex]
- This matches the difference of squares identity.

Based on the above calculations, the products that result in a difference of squares or a perfect square trinomial are:

- [tex]\((5x + 3)(5x - 3)\)[/tex]
- [tex]\((7x + 4)(7x + 4)\)[/tex]
- [tex]\((x - 9)(x - 9)\)[/tex]
- [tex]\((-3x - 6)(-3x + 6)\)[/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.