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} \end{array}

= 10−3x+5 12y

= 15−3x 12y

= 3 ( 5−x ) 4 12 y

= 5−x 4y

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} \end{array}

= 3 x+2

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)} \end{array}

= z x+3

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} \end{array}

= 8m+mn 3m × 24 n 2 −64

= m( 8+n ) 3m × 24 n 2 − 8 2

= m ( 8+n ) 3 m × 24 8 ( n−8 ) ( n+8 )

= 8 n−8