Question

q2. factorise the following expressions by taking out the factor common to both terms:
a) \\(3x + 9\\)
b) \\(5 - 15x\\)
c) \\(ab + 2a\\)
d) \\(8 + 14y\\)
e) \\(4m - 12\\)
f) \\(18m + 24\\)
g) \\(12x - 18\\)
h) \\(6a - 8\\)
i) \\(5ab - 20ac\\)
j) \\(-4x + 8\\)
k) \\(-8m - 24\\)
l) \\(5a^2 - 10a\\)

Explanation:

Find the greatest common factor for each expression

We identify the greatest common factor (GCF) of the terms in each expression:

• a) \(3x + 9\): \(\text{GCF}(3x, 9) = 3\)
• b) \(5 - 15x\): \(\text{GCF}(5, 15x) = 5\)
• c) \(ab + 2a\): \(\text{GCF}(ab, 2a) = a\)
• d) \(8 + 14y\): \(\text{GCF}(8, 14y) = 2\)
• e) \(4m - 12\): \(\text{GCF}(4m, 12) = 4\)
• f) \(18m + 24\): \(\text{GCF}(18m, 24) = 6\)
• g) \(12x - 18\): \(\text{GCF}(12x, 18) = 6\)
• h) \(6a - 8\): \(\text{GCF}(6a, 8) = 2\)
• i) \(5ab - 20ac\): \(\text{GCF}(5ab, 20ac) = 5a\)
• j) \(-4x + 8\): \(\text{GCF}(-4x, 8) = 4\) or \(-4\)
• k) \(-8m - 24\): \(\text{GCF}(-8m, -24) = 8\) or \(-8\)
• l) \(5a^2 - 10a\): \(\text{GCF}(5a^2, 10a) = 5a\)

Divide each term by the greatest common factor

We divide each term by its GCF to find the remaining terms inside the parentheses:

• a) \(3(x + 3)\)
• b) \(5(1 - 3x)\)
• c) \(a(b + 2)\)
• d) \(2(4 + 7y)\)
• e) \(4(m - 3)\)
• f) \(6(3m + 4)\)
• g) \(6(2x - 3)\)
• h) \(2(3a - 4)\)
• i) \(5a(b - 4c)\)
• j) \(-4(x - 2)\) or \(4(-x + 2)\)
• k) \(-8(m + 3)\) or \(8(-m - 3)\)
• l) \(5a(a - 2)\)

Answer:

No.	Problem	Answer
b	\(5 - 15x\)	\(5(1 - 3x)\)
c	\(ab + 2a\)	\(a(b + 2)\)
d	\(8 + 14y\)	\(2(4 + 7y)\)
e	\(4m - 12\)	\(4(m - 3)\)
f	\(18m + 24\)	\(6(3m + 4)\)
g	\(12x - 18\)	\(6(2x - 3)\)
h	\(6a - 8\)	\(2(3a - 4)\)
i	\(5ab - 20ac\)	\(5a(b - 4c)\)
j	\(-4x + 8\)	\(-4(x - 2)\)
k	\(-8m - 24\)	\(-8(m + 3)\)
l	\(5a^2 - 10a\)	\(5a(a - 2)\)