## RS Aggarwal Class 8 Solutions Chapter 6 Operations on Algebraic Expressions Ex 6B

These Solutions are part of RS Aggarwal Solutions Class 8. Here we have given RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6B.

**Other Exercises**

- RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6A
- RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6B
- RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6C
- RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6D
- RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6E

**Find each of the following products?**

**Question 1.**

**Solution:**

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

= 15x^{2} + 20x + 21x + 28 = 15x^{2} + 41x + 28 Ans.

**Question 2.**

**Solution:**

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

= 4x^{2} – 24x + 9x – 54

= 4x^{2} – 15x – 54 Ans.

**Question 3.**

**Solution:**

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

= 8x^{2} – 6x + 20x – 15

= 8x^{2} + 14x – 15 Ans.

**Question 4.**

**Solution:**

(3y – 8) X (5y – 1) = 3y(5y – 1) – 8(5y – 1)

= 15y^{2} – 3y – 40y + 8

= 15y^{2} – 43y + 8 Ans.

**Question 5.**

**Solution:**

(7x + 2y) X (x + 4y)

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

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

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

**Question 6.**

**Solution:**

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

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

= 36x^{2} + 47xy + 15y^{2} Ans.

**Question 7.**

**Solution:**

(3m – 4n) X (2m – 3n)

= 3m(2m – 3n) – 4n(2m – 3n)

= 6m^{2} – 9mn – 8mn + 12n^{2}

= 6m^{2} – 17mn + 12n^{2} Ans.

**Question 8.**

**Solution:**

(x^{2} – a^{2}) X (x – a)

= x^{2}(x – a) – a^{2}(x – a)

= x^{3} – x^{2}a – xa^{2} + a^{3} Ans.

**Question 9.**

**Solution:**

(x^{2} – y^{2}) X (x + 2y)

= x^{2}(x + 2y) – y^{2}(x + 2y)

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

**Question 10.**

**Solution:**

(3p^{2} + q^{2}) X (2p^{2} – 3q^{2})

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

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

= 6p^{4} – 7p^{2}q^{2} – 3q^{4} Ans.

**Question 11.**

**Solution:**

(2x^{2} – 5y^{2}) X (x^{2} + 3y^{2})

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

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

= 2x^{4} + x2y^{2} – 15y^{4} Ans.

**Question 12.**

**Solution:**

(x^{3} – y^{3}) X (x^{2} + y^{2})

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

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

**Question 13.**

**Solution:**

(x^{4} + y^{4}) X (x^{2} – y^{2})

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

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

**Question 14.**

**Solution:**

\(\left( { x }^{ 4 }+\frac { 1 }{ { x }^{ 4 } } \right) \times \left( { x+ }\frac { 1 }{ { x } } \right)\)

**Find each of the following products:**

**Question 15.**

**Solution:**

(x^{2} – 3x + 7) X (2x + 3)

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

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

= 2x^{3} – 3x^{2} + 5x + 21 Ans.

**Question 16.**

**Solution:**

(3x^{2} + 5x – 9) X (3x – 5)

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

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

= 9x^{3} – 52x + 45 Ans.

**Question 17.**

**Solution:**

(x^{2} – xy + y^{2}) X (x + y)

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

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

= x^{3} + y^{3} Ans.

**Question 18.**

**Solution:**

(x^{2} + xy + y^{2}) X (x – y)

(x^{2} + xy + y^{2}) X x + (x^{2} + xy + y^{2}) X ( – y)

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

= x^{3} – y^{3} Ans.

**Question 19.**

**Solution:**

(x^{3} – 2x^{2} + 5) X (4x – 1)

= (x^{3} – 2x^{2} + 5) X 4x + (x^{3} – 2x^{2} + 5) X ( – 1)

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

= 4x^{4} – 9x^{3} + 2x^{2} + 20x – 5 Ans.

**Question 20.**

**Solution:**

(9x^{2} – x + 15) X (x^{2} – 3)

(9x^{2} – X + 15) X x^{2} + (9x^{2} – x + 15) X ( – 3)

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

= 9x^{4} – x^{3} – 12x^{2} + 3x – 45 Ans.

**Question 21.**

**Solution:**

(x^{2} – 5x + 8) X (x^{2} + 2)

= (x^{2} – 5x + 8) X x^{2} + (x^{2} – 5x + 8) X 2

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

= x^{4} – 5x^{3} + 10x^{2} – 10x + 16 Ans.

**Question 22.**

**Solution:**

(x^{3} – 5x^{2} + 3x + 1) X (x^{2} – 3)

= (x^{3} – 5x^{2} + 3x + 1) X x^{2} + (x^{3} – 5x^{2} + 3x + 1) X ( – 3)

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

= x^{5} – 5x^{4} + 16x^{2} – 9x – 3 Ans.

**Question 23.**

**Solution:**

(3x + 2y – 4) X (x – y + 2)

**Question 24.**

**Solution:**

(x^{2} – 5x + 8) X (x^{2} + 2x – 3)

**Question 25.**

**Solution:**

(2x^{2} + 3x – 7) X (3x^{2} – 5x + 4)

**Question 26.**

**Solution:**

(9x^{2} – x + 15) X (x^{2} – x – 1)

Hope given RS Aggarwal Solutions Class 8 Chapter 6 Operations on Algebraic Expressions Ex 6B are helpful to complete your math homework.

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