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 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: \((3x - 5)(5 - 3x)=-(3x - 5)(3x - 5)=-(3x - 5)^2=-9x^2 + 30x - 25\). This is a negative of a perfect square trinomial, not a perfect square trinomial itself.
• Option 3: \((3x - 5)(3x + 5)=(3x)^2-5^2 = 9x^2-25\) (using difference of squares \(a^2 - b^2=(a - b)(a + b)\)), which is a binomial, not a trinomial.
• Option 4: \((3x - 5)(-3x - 5)=-(3x - 5)(3x + 5)=-(9x^2-25)=-9x^2 + 25\), which is a binomial (after simplification), not a trinomial.

Answer:

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