Factorise the following by taking out the common factor(i) 18xy – 12

1.	Factorise the following by taking out the common factor(i) 18xy – 12yz(ii) 9x5y3 + 6x3y2 – 18x2y(iii) x(b – 2c) + y(b – 2c)(iv) (ax + ay) + (bx + by)(v) 2x2(4x – 1) – 4x + 1
Answer» (i) 18xy – 12yz = (2 × 3 × 3 × y × x) – (2 × 2 × 3 × y × z) Taking out the common factors 2, 3, y, we get = 2 × 3 × y (3x – 2z) = 6y (3x- 2z) (ii) 9x⁵y³ + 6x³y² – 18x²y = (3 × 3 × x² × x³ × y × y²) + (2 × 3 × x² × x × y × y) Taking out the common factors 3, x², y, we get = 3 × x² × y (3x³ y² + 2xy – 6) = 3x²y (3x³ y² + 2xy – 6) (iii) x(b – 2c) + y(b – 2c) Taking out the binomial factor (b – 2c) from each term, we have = (b – 2c)(x + y) (iv) (ax + ay) + (bx + by) Taking at ‘a’ from the first term and ‘b’ from the second term we have (ax + ay) + (bx + by) = a (x + y) + b (x + y) Now taking out the binomial factor (x + y) from each term = (x + y)(a + b) (v) 2x²(4x – 1) – 4x + 1 Taking out -1 from last two terms 2x² (4x – 1) – 4x + 1 = 2x² (4x – 1) – 1 (4x- 1) Taking out the binomial factor 4x – 1, we get = (4x – 1)(2x² – 1)

Factorise the following by taking out the common factor(i) 18xy – 12yz(ii) 9x5y3 + 6x3y2 – 18x2y(iii) x(b – 2c) + y(b – 2c)(iv) (ax + ay) + (bx + by)(v) 2x2(4x – 1) – 4x + 1

Answer»

(i) 18xy – 12yz

= (2 × 3 × 3 × y × x) – (2 × 2 × 3 × y × z)

Taking out the common factors 2, 3, y, we get

= 2 × 3 × y (3x – 2z) = 6y (3x- 2z)

(ii) 9x⁵y³ + 6x³y² – 18x²y

= (3 × 3 × x² × x³ × y × y²) + (2 × 3 × x² × x × y × y)

Taking out the common factors 3, x², y, we get

= 3 × x² × y (3x³ y² + 2xy – 6)

= 3x²y (3x³ y² + 2xy – 6)

(iii) x(b – 2c) + y(b – 2c)

Taking out the binomial factor (b – 2c) from each term, we have

= (b – 2c)(x + y)

(iv) (ax + ay) + (bx + by)

Taking at ‘a’ from the first term and ‘b’ from the second term we have

(ax + ay) + (bx + by) = a (x + y) + b (x + y)

Now taking out the binomial factor (x + y) from each term

= (x + y)(a + b)

(v) 2x²(4x – 1) – 4x + 1

Taking out -1 from last two terms

2x² (4x – 1) – 4x + 1 = 2x² (4x – 1) – 1 (4x- 1)

Taking out the binomial factor 4x – 1, we get

= (4x – 1)(2x² – 1)