## RS Aggarwal Class 7 Solutions Chapter 6 Algebraic Expressions Ex 6D

These Solutions are part of RS Aggarwal Solutions Class 7. Here we have given RS Aggarwal Solutions Class 7 Chapter 6 Algebraic Expressions Ex 6D.

**Other Exercises**

- RS Aggarwal Solutions Class 7 Chapter 6 Algebraic Expressions Ex 6A
- RS Aggarwal Solutions Class 7 Chapter 6 Algebraic Expressions Ex 6B
- RS Aggarwal Solutions Class 7 Chapter 6 Algebraic Expressions Ex 6C
- RS Aggarwal Solutions Class 7 Chapter 6 Algebraic Expressions Ex 6D

**Find each of the following products.**

**Question 1.**

**Solution:**

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

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

= 5x x 3x + 5x x 4 + 7 x 3x + 7 x 4

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

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

**Question 2.**

**Solution:**

(4x – 3) (2x + 5)

= 4x (2x + 5) – 3 (2x + 5)

= 4x x 2x + 4x x 5 – 3 x 2x -3 x 5

= 8x^{2} + 20x – 6x – 15

= 8x^{2} + 14x – 15

**Question 3.**

**Solution:**

(x – 6) (4x + 9)

= x (4x + 9) – 6 (4x + 9)

= x x 4x + x x 9 – 6 x 4x – 6 x 9

= 4x^{2} + 9x – 24x – 54

= 4x^{2} – 15x – 54

**Question 4.**

**Solution:**

(5y – 1) (3y – 8)

= 5y x 3y – 5y x 8 – 1 x 3y – 8 x (-1)

= 15y^{2} – 40y – 3y + 8

= 15y^{2} – 43y + 8

**Question 5.**

**Solution:**

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

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

= 7x x x + 7x x 4y + 2y x x + 2y x 4y

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

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

**Question 6.**

**Solution:**

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

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

= 9x x 4x + 9x x 3y + 5y x 4x + 5y x 3y

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

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

**Question 7.**

**Solution:**

(3m – 4n) (2m – 3n)

= 3m (2m – 3n) – 4n (2m – 3n)

= 3m x 2m – 3m x 3n – 4n x 2m – 4n x (-3n)

= 6m^{2} – 9mn – 8mn + 12n^{2}

= 6m^{2} – 17mn + 12n^{2}

**Question 8.**

**Solution:**

(0.8x – 0.5y) (1.5x – 3y)

= 0.8x (1.5x – 3y) – 0.5y (1.5x – 3y)

= 0.8x x 1.5x – 0.8x x 3y – 0.5y x 1.5x – 0.5y x (-3y)

= 1.20x^{2} – 2.4xy – 0.75xy + 1.5y^{2}

= 1.2x^{2} – 3.15xy + 1.5y^{2}

**Question 9.**

**Solution:**

**Question 10.**

**Solution:**

**Question 11.**

**Solution:**

**Question 12.**

**Solution:**

(x^{2} – a^{2}) (x – a)

= x^{2} (x – a) – a^{2} (x – a)

= x^{2} x x – x^{2} x a – a^{2} x x – a^{2} (-a)

= x^{3} – x^{2 }a – xa^{2} + a^{3}

**Question 13.**

**Solution:**

(3p^{2} + q^{2}) (2p^{2} – 3q^{2})

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

= 3p^{2} x 2p^{2} – 3p^{2} x 3q^{2} + q^{2} x 2p^{2} – q^{2} x 3q^{2}

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

= 6p^{4} – 7p^{2}q^{2} – 3q^{4}

**Question 14.**

**Solution:**

(2x^{2} – 5y^{2}) (x^{2} + 3y^{2})

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

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

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

= 2y^{4} + x^{2 }y^{2} – 15y^{4}

**Question 15.**

**Solution:**

(x^{3} – y^{3}) (x^{2} + y^{2})

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

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

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

**Question 16.**

**Solution:**

(x^{4} + y^{4}) (x^{2} – y^{2})

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

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

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

**Question 17.**

**Solution:**

**Question 18.**

**Solution:**

(x^{2} – y^{2}) (x + 2y)

= x^{2} (x + 2y) – y^{2} (x + 2y)

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

= x^{3} + 2x^{2 }y – xy^{2} – 2y^{3}

**Question 19.**

**Solution:**

(2x + 3y – 5) (x + y)

= 2x (x + y) + 3y (x + y) – 5 (x + y)

= 2x x x + 2x x y + 3y x x + 3y x y – 5 x x – 5 x y

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

= 2x^{2} + 5xy + 3y^{2} – 5x – 5y

**Question 20.**

**Solution:**

(3x + 2y – 4) (x – y)

= 3x (x – y) + 2y (x – y) – 4 (x – y)

= 3x x x – 3x x y + 2y x x – 2y x y – 4 x x – 4 x (-y)

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

= 3x^{2} – xy – 2y^{2} – 4x + 4y

**Question 21.**

**Solution:**

(x^{2} – 3x + 7) (2x + 3)

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

= x^{2} x 2x + x^{2} x 3 – 3x x 2x – 3x x 3 + 7 x 2x + 7 x 3

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

= 2x^{3} – 3x^{2} + 5x + 21

**Question 22.**

**Solution:**

(3x^{2} + 5x – 9) (3x – 9)

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

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

= 9x^{3} – 27x^{2} + 15x^{2} – 45x – 27x + 81

= 9x^{3} – 12x^{2} – 72x + 81

**Question 23.**

**Solution:**

(9x^{2} – x + 15) (x^{2} – 3)

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

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

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

= 9x^{4} – x^{3} – 12x^{2} + 3x – 45

**Question 24.**

**Solution:**

(x^{2} + xy + y^{2}) (x – y)

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

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

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

= x^{3} – y^{3}

**Question 25.**

**Solution:**

(x^{2} – xy + y^{2}) (x + y)

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

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

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

**Question 26.**

**Solution:**

(x^{2} – 5x + 8) (x^{2} + 2)

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

= x^{2} x x^{2} + x^{2} x 2 – 5x x x^{2} – 5x x 2 + 8 x x^{2} + 8 x 2

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

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

= x^{4} – 5x^{3} + 10x^{2} – 10x + 16

**Simplify:**

**Question 27.**

**Solution:**

(3x + 4) (2x – 3) + (5x – 4) (x + 2)

= [3x (2x – 3) + 4 (2x – 3)] + [5x (x + 2) – 4 (x + 2)]

= [3x x 2x – 3x x 3 + 4 x 2x – 4 x 3] + [5x x x + 5x x 2 – 4 x x – 4 x 2]

= [6x^{2} – 9x + 8x – 12] + [5x^{2} + 10x – 4x – 8]

= (6x^{2} – x – 12) + (5x^{2} + 6x – 8)

= 6x^{2} – x – 12 + 5x^{2} + 6x – 8

= 6x^{2} + 5x^{2} – x + 6x – 12 – 8

= 11x^{2} + 5x – 20

**Question 28.**

**Solution:**

(5x – 3) (x + 4) – (2x + 5) (3x – 4)

= [5x x x + 5x x 4 – 3 x x – 3 x 4] – [2x x 3x + 2x x (-4) + 5 x 3x + 5x (-4)]

= [5x^{2} + 20x – 3x – 12] – [6x^{2} – 8x + 15x – 20]

= (5x^{2} + 17x – 12) – (6x^{2} + 7x – 20)

= 5x^{2} + 17x – 12 – 6x^{2} – 7x + 20

= 5x^{2} – 6x^{2} + 17x – 7x – 12 + 20

= -x^{2} + 10x + 8

**Question 29.**

**Solution:**

(9x – 7) (2x – 5) – (3x – 8) (5x – 3)

= [9x (2x – 5) -7 (2x – 5)] – [3x (5x – 3) -8 (5x – 3)]

= [9x x 2x – 9x x 5 – 7 x 2x – 7 x (-5)] – [3x x 5x – 3x x 3 – 8 x 5x – 8 x (-3)]

= [18x^{2} – 45x – 14x + 35] – [15x^{2} – 9x – 40x + 24]

= 18x^{2} – 45x – 14x + 35 – 15x^{2} + 9x + 40x – 24

= 18x^{2} – 15x^{2} – 45x – 14x + 9x + 40x + 35 – 24

= 3x^{2} – 59x + 49x + 11

= 3x^{2} – 10x + 11

**Question 30.**

**Solution:**

(2x + 5y) (3x + 4y) – (7x + 3y) (2x + y)

= [2x (3x + 4y) + 5y (3x + 4y)] – [7x (2x + y) + 3y (2x + y)]

= [2x x 3x + 2x x 4y + 5y x 3x + 5y x 4y] – [7x x 2x + 7x x y + 3y x 2x + 3y x y]

= [6x^{2} + 8xy + 15xy + 20y^{2}] – [14x^{2} + 7xy + 6xy + 3y^{2}]

= [6x^{2} + 23xy + 20y^{2}] – [14x^{2} + 13xy + 3y^{2]}

= 6x^{2} + 23xy + 20y^{2} – 14x^{2} – 13xy – 3y^{2}

= 6x^{2} – 14x^{2} + 23xy – 13xy + 20y^{2} – 3y^{2}

= -8x^{2} + 10xy + 11y^{2}

**Question 31.**

**Solution:**

(3x^{2} + 5x – 7) (x – 1) – (x^{2} – 2x + 3) (x + 4)

= [3x^{2} (x – 1) + 5x (x – 1) – 7 (x – 1)] – [x^{2} (x + 4) – 2x (x + 4) + 3 (x + 4)]

= [3x^{2} x x – 3x^{2} x 1 + 5x x x – 5x x (-1) – 7 x x -7 x (-1)] -[x^{2} x x + x^{2} x 4 – 2x x x – 2x x 4 + 3 x x + 3 x 4]

= [3x^{3} – 3x^{2} + 5x^{2} – 5x – 7x + 7] – [x^{3} + 4x^{2} – 2x^{2} – 8x + 3x + 12]

= [3x^{3} + 2x^{2} – 12x + 7] – [x^{3} + 2x^{2} – 5x + 12]

= 3x^{3} + 2x^{2} – 12x + 7 – x^{3} – 2x^{2} + 5x – 12

= 3x^{3} – x^{3} + 2x^{2} – 2x^{2} – 12x + 5x – 12 + 7

= 2x^{3} – 7x – 5

Hope given RS Aggarwal Solutions Class 7 Chapter 6 Algebraic Expressions Ex 6D are helpful to complete your math homework.

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