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ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.5

Question 1.
Work out the following divisions:
(i) (35x + 28) ÷ (5x + 4)
(ii) 7p²q²(9r – 27) ÷ 63pq(r – 3)
Solution:

Question 2.
Divide as directed:
(i) 6(2x + 7) (5x – 3) ÷ 3(5x – 3)
(ii) 33pq (p + 3) (2q – 5) ÷ 11p (2q – 5)
Solution:

Question 3.
Factorise the expression and divide them as directed:
(i) (7x² – 63x) ÷ 7(x – 3)
(ii) (3p² + 17p + 10) ÷ (p + 5)
(iii) 10xy(14y² + 43y – 21) ÷ 5x(7y – 3)
(iv) 12pqr(6p² – 13pq + 6q²) ÷ 6pq(2p – 3q)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.4

Factorise the following (1 to 11) polynomials:
Question 1.
(i) x² + 3x + 2,
(ii) z² + 10z + 24
Solution:

Question 2.
(i) y² – 7y + 12
(ii) m² – 23m + 42
Solution:

Question 3.
(i) y² – 5y – 24,
(ii) t² + 23t – 108
Solution:

Question 4.
(i) 3x² + 14x + 8,
(ii) 3y² + 10y + 8
Solution:

Question 5.
(i) 14x² – 23x + 8,
(ii) 12x² – x – 35
Solution:

Question 6.
(i) 6x² + 11x – 10
(ii) 5 – 4x – 12x²
Solution:

Question 7.
(i) 1 – 18y – 63y²,
(ii) 3x² – 5xy – 12y²
Solution:

Question 8.
(i) x² – 3xy – 40y²
(ii) 10p²q² – 21pq + 9
Solution:

Question 9.
(i) 2a²b² + ab – 45
(ii) x (12x + 7) – 10
Solution:

Question 10.
(i) (a + b)² – 11(a + b) – 42
(ii) 8 + 6(p + q) – 5(p + q)
Solution:

Question 11.
(i) (x – 2y)² – 6(x – 2y) + 5
(ii) 7 + 10(2x – 3y) – 8(2x – 3y)²
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.3

Question 1.
Factorise the following expressions using algebraic identities:
(i) x² – 12x + 36
(ii) 36p² – 60pq + 25q²
(iii) 9y² + 66xy + 121y²
(iv) a⁴ + 6a²b² + 9b⁴
(v) x² + \(\frac{1}{x^{2}}\) + 2
(vi) x² + x + \(\frac{1}{4}\)
Solution:

Factorise the following (2 to 13) expressions:
Question 2.
(i) 4p² – 9
(ii) 4x² – 169y²
Solution:

Question 3.
(i) 9x²y² – 25
(ii) 16x² – \(\frac{1}{144}\)
Solution:

Question 4.
(i) 20x² – 45y²
(ii) \(\frac{9}{16}\) – 25a²b²
Solution:

Question 5.
(i) (2a + 3b)² – 16c²
(ii) 1 – (b – c)²
Solution:

Question 6.
(i) 9 (x + y)² – x²
(ii) (2m + 3n)² – (3m + 2n)²
Solution:

Question 7.
(i) 25 (a + b)² – 16 (a – b)²
(ii) 9 (3x + 2)² – 4 (2x – 1)²
Solution:

Question 8.
(i) x³ – 25x
(ii) 63p²q² – 7
Solution:

Question 9.
(i) 32a²b – 72b³
(ii) 9 (a + b)³ – 25 (a + b)
Solution:

Question 10.
(i) x² – y² – 2y – 1
(ii) p²– 4pq + 4q² – r²
Solution:

Question 11.
(i) 9x² – y² + 4y – 4
(ii) 4a² – 4b² + 4a + 1
Solution:

Question 12.
(i) 625 – p⁴
(ii) 5y⁵ – 405y
Solution:

Question 13.
(i) x⁴ – y⁴ + x² – y²
(ii) 64a² – 9b² + 42bc – 49c²
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.2

Factorise the following (1 to 11) polynomials:
Question 1.
(i) x² + xy – x – y
(ii) y² – yz – 5y + 5z
Solution:

Question 2.
(i) 5xy + 7y – 5y² – 7x
(ii) 5p² – 8pq – 10p + 16q
Solution:

Question 3.
(i) a²b – ab² + 3a – 3b
(ii) x³ – 3x² + x – 3
Solution:

Question 4.
(i) 6xy² – 3xy – 10y + 5
(ii) 3ax – 6ay – 8by + 4bx
Solution:

Question 5.
(i) x² + xy (1 + y) + y³
(ii) y² – xy (1 – x) – x³
Solution:

Question 6.
(i) ab² + (a – 1) b – 1
(ii) 2a – 4b – xa + 2bx
Solution:

Question 7.
(i) 5ph – 10qk + 2rph – 4qrk
(ii) x² – x(a + 2b) + 2a²
Solution:

Question 8.
(i) ab (x² + y²) – xy (a² + b²)
(ii) (ax + by)² + (bx – ay)²
Solution:

Question 9.
(i) a³ + ab(1 – 2a) – 2b²
(ii) 3x²y – 3xy + 12x – 12
Solution:

Question 10.
(i) a²b + ab² – abc – b²c + axy + bxy
(ii) ax² – bx² + ay² – by² + az² – bz²
Solution:

Question 11.
(i) x – 1 – (x – 1)² + ax – a
(ii) ax + a²x + aby + by – (ax + by)²
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 11 Factorisation Ex 11.1

Factorise the following (1 to 8) polynomials:
Question 1.
(i) 8xy³ + 12x²y²
(ii) 15ax³ – 9ax²
Solution:

Question 2.
(i) 21 py² – 56py
(ii) 4x³ – 6x²
Solution:

Question 3.
(i) 25abc² – 15a²b²c
(ii) x²yz + xy²z + xyz²
Solution:

Question 4.
(i) 8x³ – 6x² + 10x
(ii) 14mn + 22m – 62p
Solution:

Question 5.
(i) 18p²q² – 24pq² + 30p²q
(ii) 27a³b³ – 18a²b³ + 75a³b²
Solution:

Question 6.
(i) 15a (2p – 3p) – 106 (2p – 3q)
(ii) 3a (x² + y²) + 6b (x² + y²)
Solution:

Question 7.
(i) 6(x + 2y)³ + 8(x + 2y)²
(ii) 14(a – 3b)³ – 21p(a – 3b)
Solution:

Question 8.
10a (2p + q)³ – 15b (2p + q)² + 35(2p + q)
Solution:

ML Aggarwal Class 8 Solutions for ICSE Maths