Respuesta :
Answer:
It's the last choice.
Step-by-step explanation:
1. (3x - 2y)(3x -2y)
= 9x^2 - 12xy + 4y^2
The product is (9x^2 - 4y^2) (9x^2 - 12xy + 4y^2)
which is neither a difference of 2 squares or perfect square trinomial.
2. (3x - 2y)(3x + 2y)
= 9x^2 - 6xy + 6xy - 4y^2
= 9x^2 - 4y^2
and (9x^2 - 4y^2(9x^2 - 4y^2) is a perfect square.
Statement 4 is true about the product (9x² – 4y²)(3x – 2y) that if it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial. This can be obtained by multiplying the product in the question with each term in the question and check whether the it is a difference of squares or a perfect square trinomial.
What is difference of square formula?
Difference of squares can be factored using the identity
a²-b²=(a+b)(a-b)
What is perfect square trinomial ?
Algebraic expressions in which there are three terms that can be obtained by multiplying a binomial with itself.
Formulas required,
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
Which statement is true?
Given product is, (9x² – 4y²)(3x – 2y)
Using difference of squares it can be written as, ((3x)² – (2y)²)(3x – 2y)
=(3x + 2y)(3x – 2y)(3x – 2y)
=(3x + 2y)(3x – 2y)²
- Statement 1: multiplied by (3x – 2y)
(3x + 2y)(3x – 2y)²× (3x – 2y)
=(3x + 2y)(3x – 2y)³
This is not in the form of difference of squares.
- Statement 2: multiplied by (3x – 2y)
(3x + 2y)(3x – 2y)²× (3x – 2y)
=(3x + 2y)(3x – 2y)³
This is not in the form of a perfect square trinomial.
- Statement 3: multiplied by (3x + 2y)
(3x + 2y)(3x – 2y)²× (3x + 2y)
=(3x + 2y)(3x – 2y)³
This is not in the form of difference of squares.
- Statement 4: multiplied by (3x + 2y)
(3x + 2y)(3x – 2y)²× (3x + 2y)
=(3x + 2y)²(3x – 2y)²
=[(3x + 2y)(3x – 2y)][(3x + 2y)(3x – 2y)]
=(9x² – 4y²)(9x² – 4y²)
=(9x² – 4y²)² = (a - b)², where a = 9x² and b = 4y²
This is in the form of a perfect square trinomial.
Hence statement 4 is true about the product (9x² – 4y²)(3x – 2y) that if it is multiplied by (3x + 2y), the product of all of the terms will be a perfect square trinomial.
Learn more about polynomials here:
brainly.com/question/11801811
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