Maharashtra Board Solutions Class 8-Maths (Practice Set 5.1): Chapter 5- Expansion Formulae

Class 8: Maths Chapter 5 solutions. Complete Class 8 Maths Chapter 5 Notes.

Maharashtra Board Solutions Class 8-Maths (Practice Set 5.1): Chapter 5- Expansion Formulae

Maharashtra Board 8th Maths Chapter 5, Class 8 Maths Chapter 5 solutions

Question 1.
Expand :
i. (a + 2)(a – 1)
ii. (m – 4)(m + 6)
iii. (p + 8) (p – 3)
iv. (13 + x)(13 – x)
v. (3x + 4y) (3x + 5y)
vi. (9x – 5t) (9x + 3t)
vii. \left(m+\frac{2}{3}\right)\left(m-\frac{7}{3}\right)(m+23)(m−73)
viii. \left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)(x+1x)(x−1x)
ix. \left(\frac{1}{y}+4\right)\left(\frac{1}{y}-9\right)(1y+4)(1y−9)
Solution:
i. (a + 2)(a – 1)
= a² + (2 – 1) a + 2 × (-1)
..[∵ (x + A) (x + B) = x² + (A + B)x + AB]
= a² + a – 2

ii. (m – 4)(m + 6)
= m² + (- 4 + 6) m + (-4) × 6
…[∵ (x + a) (x + b) = x² + (a + b)x + ab]
= m² + 2m – 24

iii. (p + 8) (p – 3)
= p² + (8 – 3) p + 8 x (-3)
…[∵ (x + a) (x + b) = x² + (a + b)x + ab]
= p² + 5p – 24

iv. (13 + x) (13 – x)
= (13)² + (x – x) 13 + x × (-x)
…[∵ (x + a) (x + b) = x² + (a + b)x + ab]
= 169 + 0 × 13 – x²
= 169 – x²

v. (3x + 4y) (3x + 5y)
= (3x)² + (4y + 5y) 3x + 4y × 5y
…[∵ (x + a) (x + b) = x² + (a + b)x + ab]
= 9x² + 9y × 3x + 20y²
= 9x² + 27xy + 20y²

vi. (9x – 5t) (9x + 3t)
= (9x)² + [(-5t) + 3t] 9x + (-5t) × 3t
…[∵ (x + a) (x + b) = x² + (a + b)x + ab]
= 81x² + (-2t) × 9x – 15t²
= 81x² – 18xt – 15t²

vii. \left(m+\frac{2}{3}\right)\left(m-\frac{7}{3}\right)(m+23)(m−73)

viii. \left(x+\frac{1}{x}\right)\left(x-\frac{1}{x}\right)(x+1x)(x−1x)

ix. \left(\frac{1}{y}+4\right)\left(\frac{1}{y}-9\right)(1y+4)(1y−9)

Intext Questions and Activities

Question 1.
Use the above formulae to fill proper terms in the following boxes. (Textbook pg. no. 23)

1. (x + 2y)² = x² + ___ + 4y²
2. (2x – 5y)² = __ – 20xy + __
3. (101)² = (100 + 1)² = ___+ ___ + 1² = ___
4. (98)² = (100 – 2)² = 10000 – ___ + ___ = ___
5. (5m + 3n) (5m – 3n) = ___ – ___ = ___ – ___

Solution:

1. (x + 2y)² = x² + 4xy + 4y²
2. (2x – 5y)² = 4x² – 20xy + 25y²
3. (101)² = (100 + 1)² = 10000 + 200 + 1² = 10201
4. (98)² = (100 – 2)² = 10000 – 400 + 4 = 9604
5. (5m + 3n) (5m – 3n) = (5m)² – (3n)² = 25m² – 9n²

Question 2.
Expand (x + a) (x + b) using formulae for areas of a square and a rectangle. (Textbook pg. no. 23)

(x + a) (x + b) = x² + ax + bx + ab
(x + a) (x + b) = x² + (a + b) x + ab
Solution:

∴ (x + a) (x + b) = x² + ax + bx + ab
∴ (x + a) (x + b) = x² + (a + b) x + ab

Download PDF

Maharashtra Board Solutions Class 8-Maths (Practice Set 5.1): Chapter 5- Expansion Formulae

Download PDF: Maharashtra Board Solutions Class 8-Maths (Practice Set 5.1): Chapter 5- Expansion Formulae PDF

Chapterwise Maharashtra Board Solutions Class 8 Maths :

• Chapter 1- Rational and Irrational Numbers (Practice Set 1.1)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.2)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.3)
• Chapter 1- Rational and Irrational Numbers (Practice Set 1.4)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.1)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.2)
• Chapter 2- Parallel Lines and Transversals (Practice Set 2.3)
• Chapter 3- Indices and Cube Root (Practice Set 3.1)
• Chapter 3- Indices and Cube Root (Practice Set 3.2)
• Chapter 3- Indices and Cube Root (Practice Set 3.3)
• Chapter 4- Altitudes and Medians of a Triangle (Practice Set 4.1)
• Chapter 5- Expansion Formulae (Practice Set 5.1)
• Chapter 5- Expansion Formulae (Practice Set 5.2)
• Chapter 5- Expansion Formulae (Practice Set 5.3)
• Chapter 5- Expansion Formulae (Practice Set 5.4)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.1)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.2)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.3)
• Chapter 6- Factorisation of Algebraic Expressions (Practice Set 6.4)
• Chapter 7- Variation (Practice Set 7.1)
• Chapter 7- Variation (Practice Set 7.2)
• Chapter 7- Variation (Practice Set 7.3)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.1)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.2)
• Chapter 8- Quadrilateral: Constructions and Types (Practice Set 8.3)
• Chapter 9- Discount and Commission (Practice Set 9.1)
• Chapter 9- Discount and Commission (Practice Set 9.2)
• Chapter 10- Division of Polynomials (Practice Set 10.1)
• Chapter 10- Discount and Commission (Practice Set 10.2)
• Chapter 11- Statistics (Practice Set 11.1)
• Chapter 11- Statistics (Practice Set 11.2)
• Chapter 11- Statistics (Practice Set 11.3)
• Chapter 12- Equations in One Variable (Practice Set 12.1)
• Chapter 12- Equations in One Variable (Practice Set 12.2)
• Chapter 13- Congruence of Triangles (Practice Set 13.1)
• Chapter 13- Congruence of Triangles (Practice Set 13.2)
• Chapter 14- Compound Interest (Practice Set 14.1)
• Chapter 14- Compound Interest (Practice Set 14.2)
• Chapter 15- Area (Practice Set 15.1)
• Chapter 15- Area (Practice Set 15.2)
• Chapter 15- Area (Practice Set 15.3)
• Chapter 15- Area (Practice Set 15.4)
• Chapter 15- Area (Practice Set 15.5)
• Chapter 15- Area (Practice Set 15.6)
• Chapter 16- Surface Area and Volume (Practice Set 16.1)
• Chapter 16- Surface Area and Volume (Practice Set 16.2)
• Chapter 16- Surface Area and Volume (Practice Set 16.3)
• Chapter 17- Factorisation of Algebraic Expressions (Practice Set 17.1)
• Chapter 17- Factorisation of Algebraic Expressions (Practice Set 17.2)