2.2.1 Pemfaktoran dan Pecahan Algebra, Praktis Berformat PT3

2.2.1 Pemfaktoran dan Pecahan Algebra, Praktis Berformat PT3

Soalan 1:

(a)(i) Faktorkan 18a + 3

(a)(ii) Kembangan –3 (–y + 5)

(b) Ungkapkan

\frac{5}{6 y} - \frac{3 x - 5}{12 y}

sebagai satu pecahan tunggal dalam bentuk termudah.

Penyelesaian:

(a)(i) 18a + 3 = 3(6a + 1)

(a)(ii) –3 (–y + 5) = 3y – 15

(b)

\begin{array}{l} \frac{5}{6 y} - \frac{3 x - 5}{12 y} = \frac{5 \times 2}{6 y \times 2} - \frac{(3 x - 5)}{12 y} \\ = \frac{10 - 3 x + 5}{12 y} \\ = \frac{15 - 3 x}{12 y} \\ = \frac{3 (5 - x)}{412 y} \\ = \frac{5 - x}{4 y} \end{array}

Soalan 2:

(a) Kembangkan:

(i) 3 (–a + c)

(ii) –5 (a – c)

(b) Faktorkan 4x + 2

\frac{3 x + 6}{x^{2} - 4} \div \frac{x + 2}{x - 2}

Penyelesaian:

(a)(i) 3 (–a + c) = –3a + 3c

(a)(ii) –5 (a – c) = –5a + 5c

(c)

\begin{array}{l} \frac{3 x + 6}{x^{2} - 4} \div \frac{x + 2}{x - 2} = \frac{3 (x + 2)}{(x + 2) (x - 2)} \times \frac{x - 2}{x + 2} \\ = \frac{3}{x + 2} \end{array}

Soalan 3:

(a) Faktorkan:

(i) 5m + 25

(ii) 7x + 9xy

(b) Permudahkan:

\frac{4 x - 12}{4 y} \div \frac{x^{2} - 9}{y z}

Penyelesaian:

(a)(i)5m + 25 = 5 (m + 5)

(a)(ii)7x + 9xy = x (7 + 9y)

\begin{array}{l} (b) \frac{4 x - 12}{4 y} \div \frac{x^{2} - 9}{y z} = \frac{4 (x - 3)}{4 y} \times \frac{y z}{(x + 3) (x - 3)} \\ = \frac{z}{x + 3} \end{array}

Soalan 4:

Permudahkan: \frac{8 m + m n}{3 m} \div \frac{n^{2} - 64}{24}

Penyelesaian:

\begin{array}{l} \frac{8 m + m n}{3 m} \div \frac{n^{2} - 64}{24} \\ = \frac{8 m + m n}{3 m} \times \frac{24}{n^{2} - 64} \\ = \frac{m (8 + n)}{3 m} \times \frac{24}{n^{2} - 8^{2}} \\ = \frac{m (8 + n)}{3 m} \times \frac{24_{8}}{(n - 8) (n + 8)} \\ = \frac{8}{n - 8} \end{array}