1 Fully factorise: \( \begin{array}{lll}\text { a } b x+c x+b y+c y & \text { b } 2 p x+3 q+2 q x+3 p & \text { c } 6 a x+3 b x+2 b+4 a \\ \text { d } a m-b n-a n+b m & \text { e } 3 d r+r-3 d s-s & \text { f } 2 a c-5 a+2 b c-5 b \\ \text { g } x^{2}+5 x+7 x+35 & \text { h } x^{2}-2 x-6 x+12 & \text { i } x^{2}+3 x+9+3 x\end{array} \)

c) \( \sqrt{2 x}-1=\sqrt{x+1} \)

Given that \( x^{2}+4 x+7=(x+p)^{2}+q \) for \( 11 x \), find the values of \( p \) and \( q \). Write lown the least possible value of \( x^{2}+4 x \) 7 and state the value of \( x \) for which is occurs.

d) \( \left[\frac{\left(\frac{x+y}{x-y}\right)^{2}-\left(\frac{x-y}{x+y}\right)^{2}}{\left(\frac{x+y}{x-y}\right)^{2}+\left(\frac{x-y}{x+y}\right)^{2}-2}\right]:\left(1+\left(\frac{x}{y}\right)^{2}\right) \)

\( f(x)=(2 x+3)^{2}-12 x \) odd or eveh?

15. Given that \( x^{2}+4 x+7=(x+p)^{2}+q \) for all \( x \), find the values of \( p \) and \( q \). Write down the least possible value of \( x^{2}+4 x \) +7 and state the value of \( x \) for which this occurs.