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


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