Question

which products result in a perfect square trinomial? select three options.

\\((-x+9)(-x-9)\\)

\\((xy+x)(xy+x)\\)

\\((2x-3)(-3+2x)\\)

\\((16-x^2)(x^2-16)\\)

\\((4y^2+25)(25+4y^2)\\)

Explanation:

Identify perfect square trinomial conditions

A perfect square trinomial results from squaring a binomial:

$$ (a+b)^2 = a^2 + 2ab + b^2 \quad \text{or} \quad (a-b)^2 = a^2 - 2ab + b^2 $$

This requires multiplying two identical binomial factors: \( (A)(B) \) where \( A = B \).

Analyze the first product

Using the Difference of Squares knowledge point

$$ (-x+9)(-x-9) = (-x)^2 - 9^2 = x^2 - 81 $$

Analyze the second product

Using the Perfect Square Trinomial and Polynomial Multiplication knowledge points

$$ (xy+x)(xy+x) = (xy+x)^2 = x^2y^2 + 2x^2y + x^2 $$

Analyze the third product

Using the Perfect Square Trinomial and Polynomial Multiplication knowledge points

$$ (2x-3)(-3+2x) = (2x-3)(2x-3) = (2x-3)^2 = 4x^2 - 12x + 9 $$

Analyze the fourth and fifth products

Using the Perfect Square Trinomial and Polynomial Multiplication knowledge points

$$
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$$

Answer:

• \((-x+9)(-x-9)\)
• \((xy+x)(xy+x)\) (Correct answer)
• \((2x-3)(-3+2x)\) (Correct answer)
• \((16-x^2)(x^2-16)\)
• \((4y^2+25)(25+4y^2)\) (Correct answer)