Page 25 - PWR UP TG2 MATHS

BAB
2 Pemfaktoran dan Pecahan Algebra

Factorisation and Algebraic Fractions

PBD
PBD 2.1 Kembangan Buku Teks
PBD
Expansion ms. 21 – 27

• Kembangan ungkapan algebra ialah hasil pendaraban satu atau dua
ungkapan dalam kurungan. Tip Penting
Expansion of algebraic expression is a product of one or two expressions in brackets.
• Kembangan ungkapan algebra boleh dilakukan dengan mendarabkan a(x + y) = ax + ay
sebutan di luar kurungan dengan setiap sebutan di dalam kurungan. (a + b)(x + y)
The expansion of algebraic expressions can be performed by multiplying the term outside of
the brackets with each term inside the brackets.
= a(x + y) + b(x + y)
= ax + ay + bx + by

1. Cari kembangan bagi setiap yang berikut berdasarkan jubin algebra yang diberi. SP 2.1.1 TP2
Find the expansion of each of the following based on the given algebraic tiles.
(a) 3x(2 + x) (b) (x + 5)(2x + 1)
5(x + 3)
2 x x 5
x 3
2x 2x 2 10x
3x 6x 3x 2
5 5x 15
1 x 5
Luas jubin
Area of tile
5(x + 3) 3x(2 + x) (x + 5)(2x + 1)
2
= 5x + 15 = 6x + 3x 2 = 2x + 10x + x + 5
2
= 2x + 11x + 5

(c) (2x + 3)(x – 2) (d) (3x – 4)(2x – 3)
(x – 1)(x + 2) 2x 3 3x
x 2 8x –12 2x – 3
x – 2 2x – 4x 3x – 6
2
x
2x
x – 1 x – x 2x – 2 2 9x – 12 12 3
2
x
1 3x – 4 4
(2x + 3)(x – 2)
2
(x – 1)(x + 2) = 2x – 4x + 3x – 6 (3x – 4)(2x – 3)
2
= x – x + 2x – 2 = 2x – x – 6 = 6x – (9x – 12) – (8x – 12) – 12
2
2
2
= x + x – 2 = 6x – 9x + 12 – 8x + 12 – 12
2
= 6x – 17x + 12
2
Tip Penting
–(a + b) = –a – b
–(a – b) = –a + b
–(–a + b) = a – b
–(–a – b) = a + b

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