To determine which products result in either a difference of squares or a perfect square trinomial, let us analyze each product one by one:
1. Product: [tex]\((5x+3)(5x-3)\)[/tex]
- This product is of the form [tex]\((a+b)(a-b)\)[/tex], which is a difference of squares.
- Therefore, [tex]\((5x+3)(5x-3)\)[/tex] results in a difference of squares.
2. Product: [tex]\((7x+4)(7x+4)\)[/tex]
- This product is of the form [tex]\((a+b)(a+b)\)[/tex], which is a perfect square trinomial.
- Therefore, [tex]\((7x+4)(7x+4)\)[/tex] results in a perfect square trinomial.
3. Product: [tex]\((2x+1)(x+2)\)[/tex]
- Neither condition of a difference of squares nor a perfect square trinomial is met with this product.
- Therefore, [tex]\((2x+1)(x+2)\)[/tex] does not result in either a difference of squares or a perfect square trinomial.
4. Product: [tex]\((4x-6)(x+8)\)[/tex]
- This product does not fit the conditions of either a difference of squares or a perfect square trinomial.
- Therefore, [tex]\((4x-6)(x+8)\)[/tex] does not result in either a difference of squares or a perfect square trinomial.
5. Product: [tex]\((x-9)(x-9)\)[/tex]
- This product is of the form [tex]\((a-b)(a-b)\)[/tex], which is a perfect square trinomial.
- Therefore, [tex]\((x-9)(x-9)\)[/tex] results in a perfect square trinomial.
6. Product: [tex]\((-3x-6)(-3x+6)\)[/tex]
- This product is of the form [tex]\((-a+b)(-a-b)\)[/tex], which simplifies to [tex]\((a-b)(a+b)\)[/tex], fitting the difference of squares form.
- Therefore, [tex]\((-3x-6)(-3x+6)\)[/tex] results in a difference of squares.
From our analysis, 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]
