# Class 8 RD Sharma Solutions – Chapter 6 Algebraic Expressions And Identities – Exercise 6.5 | Set 1

### Multiply the following:

**Question 1. (5x + 3) by (7x + 2)**

**Solution:**

To find the product of (5x + 3) (7x+2)

[use distributive property]⇒ (5x + 3) (7x + 2)

⇒ 5x(7x+2) + 3(7x+2)

⇒ (5x × 7x + 5x × 2) + (3 × 7x + 3 × 2)

⇒ 35x

^{2}+ 10x + 21x + 6⇒ 35x

^{2}+ 31x + 6The required answer is 35x

^{2}+ 31x + 6

**Question 2. (2x + 8) by (x – 3)**

**Solution:**

To find the product of (2x + 8) (x – 3)

[use distributive property]⇒ (2x+8) (x – 3)

⇒ 2x (x – 3) + 8 (x – 3)

⇒ (2x × x – 2x ×

3) + (8 × x – 8×3)⇒ (2x

^{2}– 6x) + (8x – 24)⇒ 2x

^{2}+ 2x -24The required answer is 2x

^{2}+ 2x -24

**Question 3. (7x + y) by (x + 5y)**

**Solution:**

To find the product of (7x + y) (x + 5y)

[ use distributive property ]⇒ 7x (x + 5y) + y (x + 5y)

⇒ (7x × x + 7x

×5y) + (y × x + y×5y)⇒ (7x

^{2}+ 35xy) + (xy + 5y^{2})⇒ 7x

^{2}+ 36xy + 5y^{2}The required answer is 7x

^{2}+ 36xy + 5y^{2}

**Question 4. (a – 1) by (0.1a**^{2} + 3)

^{2}+ 3)

**Solution:**

To find the product of (a – 1) (0.1a

^{2}+ 3)[use distributive property]⇒ a (0.1a

^{2}+ 3) -1(0.1a^{2}+3)⇒ 0.1a

^{3}+3a – 0.1a^{2}– 3⇒ 0.1a

^{3}– 0.1a^{2}+3a – 3The required answer is 0.1a

^{3}– 0.1a^{2}+ 3a – 3

**Question 5. (3x**^{2 }+ y^{2}) by (2x^{2 }+ 3y^{2})

^{2 }+ y

^{2}) by (2x

^{2 }+ 3y

^{2})

**Solution:**

To find the product of (3x

^{2}+ y^{2}) (2x^{2}+ 3y^{2})[use distributive property]⇒ 3x

^{2}(2x^{2}+ 3y^{2}) + y^{2}(2x^{2}+3y^{2})⇒ 6x

^{4}+ 9x^{2}y^{2}+ 2x^{2}y^{2}+ 3y^{4}⇒ 6x

^{4}+ 11x^{2}y^{2}+ 3y^{4}The required answer is 6x

^{4}+ 11x^{2}y^{2}+ 3y^{4}

**Question 6. (3/5x + 1/2y) by (5/6x + 4y)**

**Solution:**

To find the product of (3/5x +1/2y) (5/6x + 4y)

[ use distributive property ]⇒ 3/5x(5/6x + 4y) + 1/2y(5/6x + 4y)

⇒ (3/5x ×

5/6x + 3/5x × 4y) + (1/2y × 5/6x + 1/2y × 4y)⇒ 1/2x

^{2}+ 12/5xy + 5/12xy + 2y^{2}⇒ 1/2x

^{2}+ 169/60 xy + 2y^{2}The required answer is 1/2x

^{2}+ 169/60xy + 2y^{2}

**Question 7. (x**^{6 }– y^{6}) by (x^{2 }+ y^{2})

^{6 }– y

^{6}) by (x

^{2 }+ y

^{2})

**Solution:**

To find the product of (x

^{6}– y^{6}) (x^{2 }+ y^{2})[ use distributive property ]⇒ x

^{6}(x^{2}+ y^{2}) – y^{6}(x^{2 }+ y^{2})⇒ x

^{8}+ x^{6}y^{2}– y^{6}x^{2}– y^{8}The required answer is x

^{8}+ x^{6}y^{2}– y^{6}x^{2}– y^{8}

**Question 8. (x**^{2} + y^{2}) by (3a + 2b)

^{2}+ y

^{2}) by (3a + 2b)

**Solution:**

To find the product of (x

^{2}+y^{2}) (3a + 2b)[use distributive property]⇒ x

^{2}(3a + 2b) + y^{2}(3a + 2b)⇒ 3ax

^{2}+ 2bx^{2}+ 3ay^{2}+ 2by^{2}The required answer is 3ax

^{2}+ 2bx^{2}+ 3ay^{2}+ 2by^{2}

**Question 9. [-3d + (-7f)] by (5d + f)**

**Solution:**

To find the product of [-3d + (-7f)] (5d + f)

[ use distributive property ]⇒ (-3d) (5d + f) + (-7f) (5d + f)

⇒ (-15d

^{2}) + (-3df) + (-35fd) + (-7f^{2})⇒ -15d

^{2}-3df -35df -7f^{2}⇒ -15d

^{2}– 38df – 7f^{2}The required answer is -15d

^{2}– 38df -7f^{2}

**Question 10. (0.8a – 0.5b) by (1.5a – 3b)**

**Solution:**

To find the product of (0.8a – 0.5b) (1.5a – 3b)

[use distributive property]⇒ 0.8a( 1.5a -3b) – 0.5b(1.5a – 3b)

⇒

1.2a^{2}– 2.4ab – 0.75ab + 1.5b^{2}⇒ 1.2a2 + 1.5b2 – 3.15ab

The required answer is 1.2a

^{2}+ 1.5b^{2}– 3.15ab

**Question 11. (2x**^{2}y^{2} – 5xy^{2}) by (x^{2} – y^{2})

^{2}y

^{2}– 5xy

^{2}) by (x

^{2}– y

^{2})

**Solution:**

To find the product of (2x

^{2}y^{2}– 5xy^{2}) (x^{2}– y^{2})[use distributive property]⇒ 2x

^{2}y^{2}(x^{2 }– y^{2}) -5xy^{2}(x^{2}– y^{2})⇒ 2x

^{4}y^{2}– 2x^{2}y^{4}-5x^{3}y^{2}+ 5xy^{4}The required answer is 2x

^{4}y^{2 }– 2x^{2}y^{4}– 5x^{3}y^{2}+ 5xy^{4}

**Question 12. (x/7 + x**^{2}/2) by (2/5 + 9x/4)

^{2}/2) by (2/5 + 9x/4)

**Solution:**

To find the product of (x/7 + x

^{2}/2) (2/5 + 9x/4)[use distributive property]⇒ x/7(2/5 + 9x/4) + x

^{2}/2(2/5 + 9x/4)⇒ 2x/35 + 9x

^{2}/28 + x^{2}/5 + 9x^{3}/8⇒ 2x/35 + (9/28 + 1/5)x

^{2}+ 9x^{3}/8⇒ 2x/35 + (45+28/140) x

^{2 }+ 9x^{3}/8⇒ 2x/35 + 73/140x

^{2}+ 9x^{3}/8The required answer is 2x/35 + 73/140x

^{2}+ 9x^{3}/8

**Question 13. (-a/7 + a**^{2}/9) by (b/2 – b^{2}/3)

^{2}/9) by (b/2 – b

^{2}/3)

**Solution:**

To find the product of (-a/7 + a

^{2}/9) by (b/2 – b^{2}/3)[ use distributive property ]⇒ (-a/7) (b/2 -b

^{2}/3) + a^{2}/9 (b/2 – b^{2}/3)⇒ -ab/14 + ab

^{2}/21 + a^{2}b/18 – a^{2}b^{2}/27The required answer is -ab/14 + ab

^{2}/21 + a^{2}b/18 – a^{2}b^{2}/27

**Question 14. (3x**^{2}y – 5xy^{2 }) by (1/5x^{2} + 1/3y^{2})

^{2}y – 5xy

^{2 }) by (1/5x

^{2}+ 1/3y

^{2})

**Solution:**

To find the product of (3x

^{2}y -5xy^{2}) (1/5x^{2}+ 1/3y^{2})[ use distributive property ]⇒ 3x

^{2}y(1/5x^{2}+ 1/3y^{2}) -5xy^{2}(1/5x^{2}+ 1/3y^{2})⇒ 3/5x

^{4}y + x^{2}y^{3}– x^{3}y^{2}-5/3xy^{4}The required answer is 3/5x

^{4}y + x^{2}y^{3}– x^{3}y^{2}-5/3xy^{4}

**Question 15. (2x**^{2} – 1) by (4x^{3} + 5x^{2} )

^{2}– 1) by (4x

^{3}+ 5x

^{2})

**Solution:**

To find the product of (2x

^{2}– 1) (4x^{3}+ 5x^{2})[use distributive property]⇒ 2x

^{2}(4x^{3}+ 5x^{2 }) -1(4x^{3}+ 5x^{2})⇒ 8x

^{5}+10x^{4}–4x^{3}– 5x^{2}The required answer is 8x

^{5}+ 10x^{4}– 4x^{3}– 5x^{2}

**Question 16. (2xy + 3y**^{2}) by (3y^{2} – 2)

^{2}) by (3y

^{2}– 2)

**Solution:**

To find the product of (2xy + 3y

^{2}) (3y^{2}– 2)[ use distributive property ]⇒ 2xy (3y

^{2}– 2) + 3y^{2}(3y^{2}– 2)⇒ 6xy

^{3}– 4xy + 9y^{4}– 6y^{2}The required answer is 6xy

^{3}– 4xy + 9y^{4}– 6y^{2}

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