**6.2.1 Algebraic Expressions (III), PT3 Practice**

Question 1:

Question 1:

(a)(i) Factorise 18

*a*+ 3(a)(ii) Expand –3 (–

*y*+ 5)(b) Express
$\frac{5}{6y}-\frac{3x-5}{12y}$
as a single fraction in its simplest form.

Solution:Solution:

**(a)(i)**18

*a*+ 3 =

**3(6**

*a*+ 1)

**(a)(ii)**–3 (–

*y*+ 5) =

**3**

*y*– 15

**(b)**

$\begin{array}{l}\frac{5}{6y}-\frac{3x-5}{12y}=\frac{5\times 2}{6y\times 2}-\frac{\left(3x-5\right)}{12y}\\ \text{}=\frac{10-3x+5}{12y}\\ \text{}=\frac{15-3x}{12y}\\ \text{}=\frac{\overline{)3}\left(5-x\right)}{4\overline{)12}y}\\ \text{}=\frac{5-x}{4y}\end{array}$

**Question 2:**

(a) Expand:

(i) 3 (–

*a*+*c*) (ii) –5 (

*a*–*c*)(b) Factorise 4

*x*+ 2(c) Simplify:
$\frac{3x+6}{{x}^{2}-4}\xf7\frac{x+2}{x-2}$

Solution:Solution:

**(a)(i)**3 (–

*a*+

*c*) =

**–3**

*a*+ 3

**c**

**(a)(ii)**–5 (

*a*–

*c*) =

**–5**

*a*+ 5*c*

**(c)**

**Question 3:**

(a) Factorise:

(i) 5

*m*+ 25 (ii) 7

*x*+ 9*xy*(b) Simplify:
$\frac{4x-12}{4y}\xf7\frac{{x}^{2}-9}{yz}$

Solution:Solution:

**(a)(i)**5

*m*+ 25 =

**5 (**

*m*+ 5)

**(a)(ii)**7

*x*+ 9

*xy*=

*x*(7 + 9*y*)$\begin{array}{l}\text{(b)}\frac{4x-12}{4y}\xf7\frac{{x}^{2}-9}{yz}=\frac{\overline{)4}\overline{)\left(x-3\right)}}{\overline{)4}\overline{)y}}\times \frac{\overline{)y}z}{\left(x+3\right)\overline{)\left(x-3\right)}}\\ \text{}=\frac{z}{x+3}\end{array}$

**Question 4:**

(a) Factorise completely:

4 – 100

*n*^{2}(b) Express
$\frac{4}{5x}-\frac{7-10y}{15x}$
as a single fraction in its simplest form.

Solution:Solution:

**(a)**

4 – 100

*n*^{2}=**(2 + 10***n*)(2 – 10*n*)**(b)**

$\begin{array}{l}\frac{4}{5x}-\frac{7-10y}{15x}=\frac{4\times 3}{5x\times 3}-\frac{\left(7-10y\right)}{15x}\\ \text{}=\frac{12-7+10y}{15x}\\ \text{}=\frac{5+10y}{15x}\\ \text{}=\frac{\overline{)5}\left(1+2y\right)}{3\overline{)15}x}\\ \text{}=\frac{1+2y}{3x}\end{array}$

**Question 5:**

(a) Simplify:

(

*m*– 4*n*)(*m*+ 4*n*) –*m*^{2}$\frac{3x-3y}{x+y}\times \frac{2x+2y}{6x}$
(b) Simplify:

Solution:Solution:

**(a)**

(

*m*– 4*n*)(*m*+ 4*n*) –*m*^{2}=

*m*^{2 }+ 4*mn*– 4*mn*– 4*n*^{2}–*m*^{2}=

**0**

**(b)**