Chapter 5

In each case, simplify the given expression, if possible. \(8 p q+11 p q-9 p q\)

Factorise \(3 x^{3}+17 x^{2}+11 x\)

Make the specified variable the subject of the formula: (a) \(h=c+d+2 e\), for \(e\) (b) \(S=2 \pi r^{2}+2 \pi r h\), for \(h\) (c) \(Q=\sqrt{\frac{c+d}{c-d}}\), for \(c\) (d) \(\frac{x+y}{3}=\frac{x-y}{7}+2\), for \(x\)

Remove the brackets from the given expression: \((x+2)(x-2)\)

Find \(3 \times \frac{x}{11(x+y)}\).

Simplify \(\frac{x+2}{x^{2}+9 x+20} \times \frac{x+5}{x+2}\).

Factorise \(\alpha^{2}-\beta^{2}\)

Make \(n\) the subject of the formula $$ J=\frac{n E}{n L+m} $$

In each case, simplify the given expression, if possible. \( a b+a b c\)

Find \(\frac{3}{8} \times \frac{5}{7}\) without using a calculator.