Question

which will result in a perfect square trinomial?
(3x - 5)(3x - 5)
(3x - 5)(5 - 3x)
(3x - 5)(3x + 5)
(3x - 5)(-3x - 5)

Explanation:

Step1: Recall perfect square trinomial formula

A perfect square trinomial is of the form \((a - b)^2=a^2 - 2ab + b^2\) or \((a + b)^2=a^2+2ab + b^2\), which comes from squaring a binomial (multiplying a binomial by itself).

Step2: Analyze each option

• Option 1: \((3x - 5)(3x - 5)=(3x - 5)^2\). Using the formula \((a - b)^2=a^2-2ab + b^2\) where \(a = 3x\) and \(b = 5\), we get \((3x)^2-2\times(3x)\times5+5^2=9x^2-30x + 25\), which is a perfect square trinomial.
• Option 2: \((3x - 5)(5 - 3x)=-(3x - 5)(3x - 5)=-(3x - 5)^2\). This is a negative of a perfect square, not a perfect square trinomial in the standard form (it will have a negative leading coefficient for the square part and the middle term sign will be different from the perfect square trinomial form).
• Option 3: \((3x - 5)(3x + 5)=(3x)^2-5^2=9x^2 - 25\) (using the difference of squares formula \((a - b)(a + b)=a^2 - b^2\)), which is a binomial, not a trinomial.
• Option 4: \((3x - 5)(-3x - 5)=(-5 + 3x)(-5 - 3x)=(-5)^2-(3x)^2=25 - 9x^2\) (using the difference of squares formula \((a + b)(a - b)=a^2 - b^2\) with \(a=-5\) and \(b = 3x\)), which is a binomial, not a trinomial.

Answer:

A. \((3x - 5)(3x - 5)\)