Class 8 Maths Practice Set 6.2 | Factorisation of Algebraic Expressions

 

📘 Lesson 6: Factorisation of Algebraic Expressions

Maharashtra State Board – Mathematics

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✏️ Practice Set 6.2

📌 Formula Used

a³ + b³ = (a + b)(a² − ab + b²)

✏️ Practice Set 6.2

1. Factorise.

(1) x³ + 64y³

x³ + 64y³ = x³ + (4y)³

Here,

a = x,   b = 4y

Using the formula:

= (x + 4y){x² − x(4y) + (4y)²}

= (x + 4y)(x² − 4xy + 16y²)

∴ Answer = (x + 4y)(x² − 4xy + 16y²)

(2) 125p³ + q³

125p³ + q³ = (5p)³ + q³

Here,

a = 5p,   b = q

Using the formula:

= (5p + q){(5p)² − (5p)q + q²}

= (5p + q)(25p² − 5pq + q²)

∴ Answer = (5p + q)(25p² − 5pq + q²)

(3) 125k³ + 27m³

125k³ + 27m³ = (5k)³ + (3m)³

Here,

a = 5k,   b = 3m

Using the formula:

= (5k + 3m){(5k)² − (5k)(3m) + (3m)²}

= (5k + 3m)(25k² − 15km + 9m²)

∴ Answer = (5k + 3m)(25k² − 15km + 9m²)

(4) 2l³ + 432m³

Take 2 common:

2l³ + 432m³ = 2(l³ + 216m³)

= 2{l³ + (6m)³}

Here,

a = l,   b = 6m

Using the formula:

= 2(l + 6m){l² − l(6m) + (6m)²}

= 2(l + 6m)(l² − 6lm + 36m²)

∴ Answer = 2(l + 6m)(l² − 6lm + 36m²)

(5) 24a³ + 81b³

Take 3 common:

24a³ + 81b³ = 3(8a³ + 27b³)

= 3{(2a)³ + (3b)³}

Here,

a = 2a,   b = 3b

Using the formula:

= 3(2a + 3b){(2a)² − (2a)(3b) + (3b)²}

= 3(2a + 3b)(4a² − 6ab + 9b²)

∴ Answer = 3(2a + 3b)(4a² − 6ab + 9b²)

(6) y³ + 1/(8y³)

y³ + 1/(8y³) = y³ + (1/(2y))³

Here,

a = y,   b = 1/(2y)

Using the formula:

= (y + 1/(2y)) {y² − y(1/(2y)) + (1/(2y))²}

= (y + 1/(2y))(y² − 1/2 + 1/(4y²))

∴ Answer = (y + 1/(2y))(y² − 1/2 + 1/(4y²))

(7) a³ + 8/a³

a³ + 8/a³ = a³ + (2/a)³

Here,

a = a,   b = 2/a

Using the formula:

= (a + 2/a){a² − a(2/a) + (2/a)²}

= (a + 2/a)(a² − 2 + 4/a²)

∴ Answer = (a + 2/a)(a² − 2 + 4/a²)

(8) 1 + q³/125

1 + q³/125 = 1³ + (q/5)³

Here,

a = 1,   b = q/5

Using the formula:

= (1 + q/5){1² − (1)(q/5) + (q/5)²}

= (1 + q/5)(1 − q/5 + q²/25)

∴ Answer = (1 + q/5)(1 − q/5 + q²/25)

✅ Final Answers

Q. No.	Factorised Form
1	(x + 4y)(x² − 4xy + 16y²)
2	(5p + q)(25p² − 5pq + q²)
3	(5k + 3m)(25k² − 15km + 9m²)
4	2(l + 6m)(l² − 6lm + 36m²)
5	3(2a + 3b)(4a² − 6ab + 9b²)
6	(y + 1/(2y))(y² − 1/2 + 1/(4y²))
7	(a + 2/a)(a² − 2 + 4/a²)
8	(1 + q/5)(1 − q/5 + q²/25)