Which products result in a perfect square trinomial? check all that apply. (–x + 9)(–x – 9) (xy + x)(xy + x) (2x – 3)(–3 + 2x) (16 – x2)(x2 – 16) (4y2 + 25)(25 + 4y2)

(xy + x)and (xy + x)

(2x - 3) and (-3 + 2x)

(4y² + 25) and (25 + 4y²)

Step-by-step explanation:

* Lets explain the meaning of the perfect square trinomial

- If a binomial multiply by itself, then the answer will be a perfect

 square trinomial

- Example: if the binomial (ax + b) multiply by itself, then

 (ax ± b)(ax ± b) = (ax)(ax) ± (ax)(b) ± (b)(ax) + (b)(b)

 (ax + b)(ax + b) = (ax)² ± 2(axb) + (b)²

∵ (ax + b)(ax + b) = (ax + b)²

∴ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

* From the example above the perfect square trinomial has 3 terms

# 1st term is the square the first term in the binomial

# 2nd term is twice the product of the two terms of the binomial

# 3rd term is the square of the second term of the binomial

* Lets solve the problem

- The product of (-x + 9)and (-x - 9)

∵ -x + 9 ≠ -x - 9

∴ The product of (-x + 9) and (-x - 9) is not a perfect square trinomial

- The product of (xy + x)and (xy + x)

∵ xy + x = xy + x

∴ (xy + x)(xy + x) = (xy + x)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (xy + x) and (xy + x) is a perfect square trinomial

- The product of (2x - 3) and (-3 + 2x)

∵ (-3 + 2x) can be written as (2x - 3)

∴ 2x - 3 = -3 + 2x

∴ (2x - 3)(-3 + 2x) = (2x - 3)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (2x - 3)(-3 + 2x) is a perfect square trinomial

- The product of (16 - x²) and (x² - 16)

∵ 16 - x² can be written as -x² + 16

- If we take -1 common factor from -x² + 16

∴ -x² + 16 = -(x² - 16)

∴ (-x² + 16)(x² - 16) = -(x² - 16)(x² - 16) = -(x² - 16)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∵ -(x² - 16)² = -(x^4 - 32x² + 256) = -x^4 + 32x² - 256

∵ x^4 - 32x² + 256 is perfect square trinomial

∵ -x^4 + 32x² - 256 is not a perfect square trinomial

∴ The product of (16 - x²) and (x² - 16) is not a perfect square trinomial

- The product of (4y² + 25) and (25 + 4y²)

∵ 25 + 4y² can be written as 4y² + 25

∴ 4y² + 25 = 25 + 4y²

∴ (4y² + 25)(25 + 4y²) = (4y² + 25)²

∵ (ax ± b)² = (ax)² ± 2(axb) + (b)² ⇒ perfect square trinomial

∴ The product of (4y² + 25) and (25 + 4y²) is a perfect square trinomial