Class 8 Maths | Lesson 6: Factorisation of Algebraic Expressions | Practice Set 6.4 – Maharashtra State Board

📘 Lesson 6: Factorisation of Algebraic Expressions

Maharashtra State Board –Mathematics

✏️ Practice Set 6.4

(1)

m² − n² (m + n)² × m² + mn + n² m³ − n³

Factorise:

= (m − n)(m + n) (m + n)(m + n) × m² + mn + n² (m − n)(m² + mn + n²)

Cancel common factors:

= (m − n) (m + n) (m + n) (m + n) × m² + mn + n² (m − n)(m² + mn + n²)

= 1 m + n

∴ Answer = 1 m + n

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(2)

a² + 10a + 21 a² + 6a − 7 × a² − 1 a + 3

Factorise:

= (a + 3)(a + 7) (a + 7)(a − 1) × (a − 1)(a + 1) a + 3

Cancel common factors:

= (a + 3) (a + 7) (a + 7) (a − 1) × (a − 1)(a + 1) a + 3

= a + 1

∴ Answer = a + 1

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(3)

8x³ − 27y³ 4x² − 9y²

Using identities:

= (2x − 3y)(4x² + 6xy + 9y²) (2x − 3y)(2x + 3y)

Cancel common factor:

= (2x − 3y) (4x² + 6xy + 9y²) (2x − 3y) (2x + 3y)

= 4x² + 6xy + 9y² 2x + 3y

∴ Answer = 4x² + 6xy + 9y² 2x + 3y

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(4)

x² − 5x − 24 (x + 3)(x + 8) × x² − 64 (x − 8)²

Factorise:

= (x − 8)(x + 3) (x + 3)(x + 8) × (x − 8)(x + 8) (x − 8)(x − 8)

Cancel common factors:

= (x − 8) (x + 3) (x + 3)(x + 8) × (x − 8) (x + 8) (x − 8)(x − 8)

= 1

∴ Answer = 1

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(5)

3x² − x − 2 x² − 7x + 12 ÷ 3x² − 7x − 6 x² − 4

Factorise:

= (3x + 2)(x − 1) (x − 3)(x − 4) ÷ (3x + 2)(x − 3) (x − 2)(x + 2)

Division को multiplication by reciprocal में बदलें:

= (3x + 2)(x − 1) (x − 3)(x − 4) × (x − 2)(x + 2) (3x + 2)(x − 3)

Cancel common factors:

= (3x + 2)(x − 1) (x − 3)(x − 4) × (x − 2)(x + 2) (3x + 2) (x − 3)

= (x − 1)(x − 2)(x + 2) (x − 3)²(x − 4)

∴ Answer = (x − 1)(x − 2)(x + 2) (x − 3)²(x − 4)

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(6)

4x² − 11x + 6 16x² − 9

Factorise:

= (4x − 3)(x − 2) (4x − 3)(4x + 3)

Cancel common factor:

= (4x − 3)(x − 2) (4x − 3)(4x + 3)

= x − 2 4x + 3

∴ Answer = x − 2 4x + 3

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(7)

a³ − 27 5a² − 16a + 3 ÷ a² + 3a + 9 25a² − 1

Factorise:

= (a − 3)(a² + 3a + 9) (5a − 1)(a − 3) ÷ a² + 3a + 9 (5a − 1)(5a + 1)

Division को multiplication by reciprocal में बदलें:

= (a − 3)(a² + 3a + 9) (5a − 1)(a − 3) × (5a − 1)(5a + 1) a² + 3a + 9

Cancel common factors:

= (a − 3) (a² + 3a + 9) (5a − 1) (a − 3) × (5a − 1)(5a + 1) a² + 3a + 9

= 5a + 1

∴ Answer = 5a + 1

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(8)

1 − 2x + x² 1 − x³ × 1 + x + x² 1 + x

Factorise:

= (1 − x)(1 − x) (1 − x)(1 + x + x²) × 1 + x + x² 1 + x

Cancel common factors:

= (1 − x)(1 − x) (1 − x) (1 + x + x²) × 1 + x + x² 1 + x

After cancellation:

= 1 − x 1 + x

∴ Answer = 1 − x 1 + x