Question

One of the factors of (9x² − 1) − (1 + 3x)², is

(a) 3 + x

(b) 3 − x

(c) 3x − 1

(d) 3x + 1

Answer 1

To find all the factors of (9x² − 1) − (1 + 3x)², let us factorise it.
$$\begin{gathered} \left(9x^2-1\right)-{\left(1+3x\right)}^2=\left(9x^2-1\right)-\left(1+6x+9x^2\right)\left[\because {\left(a+b\right)}^2=a^2+2ab+b^2\right] \\ =9x^2-1-1-6x-9x^2 \\ =-2-6x \\ =-2\left(1+3x\right) \end{gathered}$$
Thus, the factors of (9x² − 1) − (1 + 3x)² are –2 and 3x + 1.
Hence, the correct option is (d).