RS Aggarwal Class 8 Math Sixth Chapter Operation on Algebric Expressions Exercise 6B Solution

RS Aggarwal Class 8 Math Sixth Chapter Operation on Algebric Expressions Exercise 6B Solution

EXERCISE 6B

Find each the following products:

(1) (5x + 7) × (3x + 4)

= (5x × 3x) + (7 × 3x) + (5x × 4) + (7 × 4)

= 15x² + 21x + 20x + 28

= 15x² + 41x + 28

(2) (4x + 9) × (x – 6)

= (4x × x) + (9 × x) – (4x × 6) – (9 × 6)

= 4x² + 9x – 24x – 54

= 4x² – 15x – 54

(3) (2x + 5) × (4x – 3)

= (2x × 4x) + (5 × 4x) – (2x × 3) – (5 × 3)

= 8x² + 20x – 6x – 15

= 8x² + 14x – 15

(4) (3y – 8) × (2m – 3n)

= (3y × 2m) – (8 × 2m) – (3y × 3n) + (8 × 3n)

= 6ym – 16m – 9yn + 24n

(5) (7x + 2y) × (x + 4y)

= (7x × x) + (2y × x) + (7x × 4y) + (2y × 4y)

= 7x² + 2xy + 28xy + 8y²

= 7x² + 30xy + 8y²

(6) (9x + 5y) × (4x × 3y)

= (9x × 4x) + (5y × 4x) + (9x × 3y) + (5y × 3y)

= 36x² + 20xy + 27xy + 15y²

(7) (3m – 4n) × (2m – 3n)

= (3m × 2m) – (4n × 2m) – (3m × 3n) + (4n × 3n)

= 6m² – 8mn – 9mn + 12n²

= 6m² – 17mn + 12n²

(8) (x² – a²) × (x – a)

= (x² × x) – (a² × x) – (x² × a) + (a² × a)

= x³ + a²x – ax² + a³

(9) (x² – y²) × (x + 2y)

= (x² × x) – (y² × x) + (x² × 2y) – (y² × y)

= x³ – xy² + 2x²y – y³

(10) (3p² + q²) × (2p² – 3q²)

= (3p² × 2p²) + (q² × 2p²) – (3p² × 3q²) – (q² × 3q²)

= 6p⁴ + 2p²q² – 9p²q² – 3q⁴

= 6p⁴ – 7p²q² – 3q⁴

(11) (2x² – 5y²) × (x² + 3y²)

= (2x² × x²) – (5y² × x²) + (2x² × 3y²) – (5y² × 3y²)

= 2x⁴ – 5x²y² + 6x²y² – 15y⁴

= 2x⁴ + x²y² – 15y⁴

(12) (x³ – y³) × (x² + y²)

= (x³ × x²) – (y³ × x²) + (x³ × y²) – (y³ × y²)

= x⁵ – x²y³ + x³y² – y⁵

(13) (x⁴ + y⁴) × (x² – y²)

= (x⁴ × x²) + (y⁴ × x²) – (x⁴ × y²) – (y⁴ × y²)

= x⁶ + x²y⁴ – x⁴y² – y⁶

Find each of the following products:

(15) (x² – 3x + 7) × (2x + 3)

= (x² × 2x) – (3x × 2x) + (7 × 2x) + (x² × 3) – (3x × 3) + (7 × 3)

= 2x³ – 6x² + 14x + 3x² – 9x + 21

= 2x³ – 3x² + 5x + 21

(16) (3x² + 5x – 9) × (3x – 5)

= (3x² × 3x) + (5x × 3x) – (9 × 3x) – (3x² × 5) – (5x × 5) + (9 × 5)

= 9x³ + 15x² – 27x – 15x² – 25x + 45

= 9x³ – 52x + 45

(17) (x² – xy + y²) × (x + y)

= (x² × x) – (xy × x) + (y² × x) + (x² × y) – (xy × y) + (y² × y)

= x³ – x²y + y²x + x²y – xy² + y³

= (x³ + y³)

(18) (x² + xy + y²) × (x – y)

= (x² × x) + (xy × x) + (y² × x) – (x² × y) – (xy × y) – (y² × y)

= x³ + x²y + xy² – x²y – xy² – y³

= (x³ – y³)

(19) (x³ – 2x² + 5) × (4x – 1)

= (x³ × 4x) – (2x² × 4x) + (5 × 4x) – x³ + 2x² – 5

= 4x⁴ – 8x³ + 20x – x³ + 2x² – 5

= 4x⁴ – 9x³ + 2x² + 20x – 5

(20) (9x² – x + 15) × (x² – 3)

= (9x² × x²) – (x × x²) + (15 × x²) – (9x² × 3) + 3x – 45

= 9x⁴ – x³ + 15x² – 27x² + 3x – 45

= 9x⁴ – x³ – 12x² + 3x – 45

(21) (x² – 5x + 8) × (x² + 2)

= (x² × x²) – (5x × x²) + 8x² + 2x² – 10x + 16

= x⁴ – 5x³ + 10x² – 10x + 16

(22) (x³ – 5x² + 3x + 1) × (x² – 3)

= (x³ × x²) – (5x² × x²) + (3x × x²) + x² – 3x³ + 15x² – 9x – 3

= x⁵ – 5x⁴ + 3x³ + x² – 3x³ + 15x² – 9x – 3

= x⁵ – 5x⁴ + 16x² – 9x – 3

(23) (3x + 2y – 4) × (x – y + 2)

= 3x² + 2xy – 4x – 3xy – 2y² + 4y + 6x + 4y – 8

= 3x² – xy + 2x – 2y² + 8y – 8

(24) (x² – 5x + 8) × (x² + 2x – 3)

= x⁴ – 5x³ + 8x² + 2x³ – 10x² + 16x – 3x² + 15x – 24

= x⁴ – 3x³ – 5x² + 31x – 24

(25) (2x² + 3x – 7) × (3x² – 5x + 4)

= 6x⁴ + 9x³ – 21x² – 10x³ – 15x² + 35x + 8x² + 12x – 28

= 6x⁴ – x³ – 28x² + 47x – 28

(26) (9x² – x + 15) × (x² – x – 1)

= 9x⁴ – x³ + 15x² – 9x³ + x² – 15x – 9x² + x – 15

= 9x⁴ – 10x³ + 7x² – 14x – 15