NCERT solution Class 8 algebraic expressions and identities

NCERT Solutions

Class 8 Maths

Algebraic Expressions and Identities

NCERT Questions

Ex.9.1 Q.1
Ex.9.1 Q.2
Ex.9.1 Q.3
Ex.9.1 Q.4
Ex.9.2 Q.1
Ex.9.2 Q.2
Ex.9.2 Q.3
Ex.9.2 Q.4
Ex.9.2 Q.5
Ex.9.3 Q.1
Ex.9.3 Q.2
Ex.9.3 Q.3
Ex.9.3 Q.4
Ex.9.3 Q.5
Ex.9.4 Q.1
Ex.9.4 Q.2
Ex.9.4 Q.3
Ex.9.5 Q.1
Ex.9.4 Q.2
Ex.9.5 Q.3
Ex.9.5 Q.4
Ex.9.5 Q.5
Ex.9.5 Q.6
Ex.9.5 Q.7
Ex.9.5 Q.8

Ex.9.5 Q.4

Simplify:

1. (a² – b²)²

2. (2x + 5)² – (2x - 5)²

3. (7m – 8n)² + (7m + 8n)²

4. (4m + 5n)² + (5m + 4n)²

5. (2.5p – 1.5q)² – (1.5p – 2.5q)²

6. (ab + bc)² – 2ab² c

7. (m² – n² m²) + 2m³ n²

1. (a² – b²)² = (a²)² – 2 × a² × b² + (b²)²

[Using (a - b)² = a² - 2ab + b²]

= a⁴ – 2a² b² + b⁴

2. (2x + 5)² – (2x - 5)² = (2x)² + 2 × 2x × 5 + (5)² - {(2x)² + 2 × 2x × 5 + (5)²}

= 4x² + 20x + 25 – (4x² - 20x + 25)

= 4x² + 20x + 25 – 4x² + 20x - 25

= 40x

3. (7m – 8n)² + (7m + 8n)²

= (7m)² - 2 × 7m × 8n + (8n)² + {(7m)² + 2 × 7m × 8n + (8n)²}

= 49m² – 112mn + 64n² + (49m² + 112mn + 64n²)

= 49m² – 112mn + 64n² + 49m² + 112mn + 64n²

= 98m² + 128n²

4. (4m + 5n)² + (5m + 4n)²

= (4m)² + 2 × 4m × 5n + (5n)² + {(5m)² + 2 × 5m × 4n + (4n)²}

= 16m² + 40mn + 25n² + 25m² + 40mn + 16n²

= 41m² + 80mn + 41n²

5. (2.5p – 1.5q)² – (1.5p – 2.5q)²

= (2.5p)² - 2 × 2.5p × 1.5q + (1.5q)² - {(1.5p)² - 2 × 1.5p × 2.5q + (2.5q)²}

= 6.25p² – 7.50pq + 2.25q² – (2.2.5p² – 7.50pq + 6.25q²)

= 6.25p² – 7.50pq + 2.25q² – 2.2.5p² + 7.50pq - 6.25q²

= 4p² – 4q²

6. (ab + bc)² – 2ab² c = (ab)² + 2 × ab × bc + (bc)² – 2ab² c

= a² b² + 2ab² c + b² c² - 2ab² c

= a² b² + b² c²

7. (m² – n² m) + 2m³ n²= (m²)² – 2 × m² × n² m + (n² m)² - 2m³ n²

= m⁴ – 2m³ n² + n⁴ m² - 2m³ n²

= m⁴ + n⁴ m²

Video solution:

Algebraic Expressions and Identities Class 8 Maths NCERT Chapter 9 NCERT Solutions

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