1. Factorise:

(i) 5x² – 20xy

Solution:

= 5x(x – 4y)

 

(ii) 2p(x + y) – 3q(x + y)

Solution:

= (x + y) (2p – 3q)

(iii) 4(a + b)² – 6(a + b)

Solution:

= 2 (a + b) [2(a + b) – 3]

= 2 (a + b) (2a + 2b – 3)

(iv) 18x²y – 24xyz

Solution:

= 6xy (3x – 4z)

(v) 7xa – 70 xb

Solution:

= 7x (a – 10b)

(vi) 13m² + 156n²

Solution:

=13(m² + 12n²)

(vii) 3x² + 6x +6

Solution:

= 3 (x² + 2x + 2)

 

(viii) 4abx² + 8abx + 120by

Solution:

= 4ab (x² + 2x +3y)

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2. Factorise

(i) x² + xy + xz + yz

Solution:

= x (x + y) + z (x+ y)

=(x + y) (x + z)

(ii) a² – ab + ac – bx

Solution:

= a (a – b) + c (a – b)

= (a – b) (a – c)

(iii) 4x + bx + 4b + b²

Solution:

= x (4 + b) + b (4 + b)

= (4 + b) (x + b)

(iv) 6ax – 6a + 5a – 5

Solution:

= 6a (x – 1) + 5 (x – 1)

= (3x + 5) (x² + 1)

(v) a³ + a²b + ab + b²

Solution:

= a² (a +b) + b (a +b)

= (a + b) (a² + b)

(vi) 3x³ + 5x² + 3x +5

Solution:

= x² (3x +5) + 1 (3x + 5)

= (3x + 5) (x² + 1)

(vii) y⁴ – 2y³ + y – 2

Solution:

= y³(y – 2) + 1 (y – 2)

= (y – 2) (y³ – 1)

= (y – 2) (y³ – 1³)

= (y – 2) (y + 1) (y² – y +1)

(viii) t⁴ + t⁴ – 2t – 2

Solution:

= t³ (t + 1) – 2(t +1)

= (t – 1) (t³ – 2)

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