# 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)

= 15x^{2} + 21x + 20x + 28

= 15x^{2} + 41x + 28

**(2) (4x + 9) × (x – 6)**

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

= 4x^{2} + 9x – 24x – 54

= 4x^{2} – 15x – 54

**(3) (2x + 5) × ****(4x – 3)**

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

= 8x^{2} + 20x – 6x – 15

= 8x^{2} + 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)

= 7x^{2} + 2xy + 28xy + 8y^{2}

= 7x^{2} + 30xy + 8y^{2}

**(6) (9x + 5y) × (4x × 3y)**

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

= 36x^{2} + 20xy + 27xy + 15y^{2}

**(7) (3m – 4n) × (2m – 3n)**

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

= 6m^{2} – 8mn – 9mn + 12n^{2}

= 6m^{2} – 17mn + 12n^{2}

**(8) (x ^{2} – a^{2}) × (x – a)**

= (x^{2} × x) – (a^{2 }× x) – (x^{2} × a) + (a^{2} × a)

= x^{3} + a^{2}x – ax^{2} + a^{3}

**(9) (x ^{2} – y^{2}) × (x + 2y)**

= (x^{2} × x) – (y^{2} × x) + (x^{2} × 2y) – (y^{2} × y)

= x^{3} – xy^{2} + 2x^{2}y – y^{3}

**(10) (3p ^{2} + q^{2}) × (2p^{2} – 3q^{2})**

= (3p^{2} × 2p^{2}) + (q^{2} × 2p^{2}) – (3p^{2} × 3q^{2}) – (q^{2} × 3q^{2})

= 6p^{4} + 2p^{2}q^{2} – 9p^{2}q^{2} – 3q^{4}

= 6p^{4} – 7p^{2}q^{2} – 3q^{4}

**(11) (2x ^{2} – 5y^{2}) × (x^{2} + 3y^{2})**

= (2x^{2} × x^{2}) – (5y^{2} × x^{2}) + (2x^{2} × 3y^{2}) – (5y^{2} × 3y^{2})

= 2x^{4} – 5x^{2}y^{2} + 6x^{2}y^{2} – 15y^{4}

= 2x^{4} + x^{2}y^{2} – 15y^{4}

**(12) (x ^{3} – y^{3}) × (x^{2} + y^{2})**

= (x^{3} × x^{2}) – (y^{3} × x^{2}) + (x^{3} × y^{2}) – (y^{3} × y^{2})

= x^{5} – x^{2}y^{3} + x^{3}y^{2} – y^{5}

**(13) (x ^{4} + y^{4}) × **

**(x**

^{2}– y^{2})= (x^{4} × x^{2}) + (y^{4} × x^{2}) – (x^{4} × y^{2}) – (y^{4} × y^{2})

= x^{6} + x^{2}y^{4} – x^{4}y^{2} – y^{6}

### Find each of the following products:

**(15) (x ^{2} – 3x + 7) × (2x + 3)**

= (x^{2} × 2x) – (3x × 2x) + (7 × 2x) + (x^{2} × 3) – (3x × 3) + (7 × 3)

= 2x^{3} – 6x^{2} + 14x + 3x^{2} – 9x + 21

= 2x^{3} – 3x^{2} + 5x + 21

**(16) (3x ^{2} + 5x – 9) × (3x – 5)**

= (3x^{2} × 3x) + (5x × 3x) – (9 × 3x) – (3x^{2} × 5) – (5x × 5) + (9 × 5)

= 9x^{3} + 15x^{2} – 27x – 15x^{2} – 25x + 45

= 9x^{3} – 52x + 45

**(17) (x ^{2} – xy + y^{2}) × (x + y)**

= (x^{2} × x) – (xy × x) + (y^{2} × x) + (x^{2} × y) – (xy × y) + (y^{2} × y)

= x^{3} – x^{2}y + y^{2}x + x^{2}y – xy^{2} + y^{3}

= (x^{3} + y^{3})

**(18) (x ^{2} + xy + y^{2}) × (x – y)**

= (x^{2} × x) + (xy × x) + (y^{2} × x) – (x^{2} × y) – (xy × y) – (y^{2} × y)

= x^{3} + x^{2}y + xy^{2} – x^{2}y – xy^{2} – y^{3}

= (x^{3} – y^{3})

**(19) (x ^{3} – 2x^{2} + 5) × (4x – 1)**

= (x^{3} × 4x) – (2x^{2} × 4x) + (5 × 4x) – x^{3} + 2x^{2} – 5

= 4x^{4} – 8x^{3} + 20x – x^{3} + 2x^{2} – 5

= 4x^{4} – 9x^{3} + 2x^{2} + 20x – 5

**(20) (9x ^{2} – x + 15) × (x^{2 }– 3)**

= (9x^{2} × x^{2}) – (x × x^{2}) + (15 × x^{2}) – (9x^{2} × 3) + 3x – 45

= 9x^{4} – x^{3} + 15x^{2} – 27x^{2} + 3x – 45

= 9x^{4} – x^{3} – 12x^{2} + 3x – 45

**(21) (x ^{2} – 5x + 8) × (x^{2} + 2)**

= (x^{2} × x^{2}) – (5x × x^{2}) + 8x^{2} + 2x^{2} – 10x + 16

= x^{4} – 5x^{3} + 10x^{2} – 10x + 16

**(22) (x ^{3} – 5x^{2} + 3x + 1) × (x^{2} – 3)**

= (x^{3} × x^{2}) – (5x^{2} × x^{2}) + (3x × x^{2}) + x^{2} – 3x^{3} + 15x^{2} – 9x – 3

= x^{5} – 5x^{4} + 3x^{3} + x^{2} – 3x^{3} + 15x^{2} – 9x – 3

= x^{5} – 5x^{4} + 16x^{2} – 9x – 3

**(23) (3x + 2y – 4) × (x – y + 2)**

= 3x^{2} + 2xy – 4x – 3xy – 2y^{2} + 4y + 6x + 4y – 8

= 3x^{2} – xy + 2x – 2y^{2} + 8y – 8

**(24) (x ^{2} – 5x + 8) × (x^{2} + 2x – 3)**

= x^{4} – 5x^{3} + 8x^{2} + 2x^{3} – 10x^{2} + 16x – 3x^{2} + 15x – 24

= x^{4} – 3x^{3} – 5x^{2} + 31x – 24

**(25) (2x ^{2} + 3x – 7) × (3x^{2} – 5x + 4)**

= 6x^{4} + 9x^{3} – 21x^{2} – 10x^{3} – 15x^{2} + 35x + 8x^{2} + 12x – 28

= 6x^{4} – x^{3} – 28x^{2} + 47x – 28

**(26) (9x ^{2} – x + 15) × (x^{2} – x – 1)**

= 9x^{4} – x^{3} + 15x^{2} – 9x^{3} + x^{2} – 15x – 9x^{2} + x – 15

= 9x^{4} – 10x^{3} + 7x^{2} – 14x – 15