Find the common factors of the given terms. 1. 12, 36 2. 2y, 22xy 3. 6abc, 24ab2, 12a2 4. 16x3, 4x2, 32x 5. 3x2y3, 10x3y2, 6x2yz 2. Factorise the following expressions: 1. 7x - 42... Find the common factors of the given terms. 1. 12, 36 2. 2y, 22xy 3. 6abc, 24ab2, 12a2 4. 16x3, 4x2, 32x 5. 3x2y3, 10x3y2, 6x2yz 2. Factorise the following expressions: 1. 7x - 42 2. 6 - 12q 3. 7a2 + 14a 4. 16z + 20z 5. 5x2y - 15xy2 6. -4a2 + 4ab - 4ca 7. a2y + bxy2 + cxyz 3. Factorise: 1. x3 + xy + 8x + 8y 2. 15xy - 6x + 5y - 2.
Understand the Problem
The question is asking to find the common factors of given terms and to factorize certain expressions. This includes different algebraic expressions and their factorization.
Answer
The GCFs are \(12, 2y, 6b, 7, 4z, 5x, 5\); factored forms are \(1(7x - 12), 7a(a + 2), 7(p + 30), (x^3 + 8)(y + 1), 3(5xy - 2x + y - \frac{2}{3})\).
Answer for screen readers
The common factors and factored forms are:
- (i) GCF is (12).
- (ii) GCF is (2y).
- (iii) GCF is (6b).
- (iv) GCF is (7).
- (v) GCF is (4z).
- (vi) GCF is (5x).
- (vii) GCF is (5).
- Factored forms:
- (i) (1(7x - 12))
- (ii) (7a(a + 2))
- (iii) (7(p + 30))
- (i) ((x^3 + 8)(y + 1))
- (ii) (3(5xy - 2x + y - \frac{2}{3}))
Steps to Solve
- Finding Common Factors of Given Terms
To find the common factors of the first set:
(i) (12, 36)
The factors of (12) are (1, 2, 3, 4, 6, 12) and the factors of (36) are (1, 2, 3, 4, 6, 9, 12, 18, 36).
The common factors are (1, 2, 3, 4, 6, 12), and the greatest common factor (GCF) is (12).
(ii) (2y, 22xy)
The factors of (2y) are (1, 2) and (y), and the factors of (22xy) are (1, 2, 11) and (x, y).
The common factors are (1, 2, y), and the GCF is (2y).
(iii) (6abc, 24b^2, 12a^2b)
The GCF is (6b).
(iv) (7x - 42) The common factor is (7).
(v) (16z + 20z^2) The common factor is (4z).
(vi) (5x^2 - 15xy^2)
The GCF is (5x).
(vii) (10a^2 - 15b^2 + 20c^2) The GCF is (5).
(viii) (x^2y + 8x + 8y) The common factor is (x + 8).
- Factoring the Given Expressions
Now, for the examples to be factored:
(i) For (7x - 12)
Factor out (1) as no other common factor exists.
(ii) For (7a^2 + 14a)
Factor out (7a):
$$7a(a + 2)$$
(iii) For (7p + 30a) Factor out (p): $$7(p + 30)$$
- Factorising Further Expressions
For the following expressions:
(i) Factor (x^3xy + 8x + 8y)
To factor this expression, rewrite groups:
$$x^3y + 8x + 8y = (x^3y + 8) + (8x + 8y) = (x^3 + 8)(y + 1)$$
(ii) (15xy - 6x + 5y - 2)
Combine like terms:
$$3(5xy - 2x + y - \frac{2}{3})$$
The common factors and factored forms are:
- (i) GCF is (12).
- (ii) GCF is (2y).
- (iii) GCF is (6b).
- (iv) GCF is (7).
- (v) GCF is (4z).
- (vi) GCF is (5x).
- (vii) GCF is (5).
- Factored forms:
- (i) (1(7x - 12))
- (ii) (7a(a + 2))
- (iii) (7(p + 30))
- (i) ((x^3 + 8)(y + 1))
- (ii) (3(5xy - 2x + y - \frac{2}{3}))
More Information
Finding common factors helps simplify expressions and solve algebraic equations more easily. This process is essential in understanding deeper algebra concepts.
Tips
- Forgetting to check for GCF when expressions appear complicated.
- Overlooking simple factors that can be factored out initially.
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