RS Aggarwal solution class 8 chapter 6 Operations on Algebraic Expressions Exercise 6B

Exercise 6B

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Question 1:

Find the product:
(5x + 7) × (3x + 4)

Answer 1:

By horizontal method:

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Question 2:

Find the product:
(4x + 9) × (x − 6)

Answer 2:

By horizontal method:

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Question 3:

Find the product:
(2x + 5) × (4x − 3)

Answer 3:

By horizontal method:

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Question 4:

Find the product:
(3y − 8) × (5y − 1)

Answer 4:

By horizontal method:

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Question 5:

Find the product:
(7x + 2y) × (x + 4y)

Answer 5:

By horizontal method:

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Question 6:

Find the product:
(9x + 5y) × (4x + 3y)

Answer 6:

By horizontal method:

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Question 7:

Find the product:
(3m − 4n) × (2m − 3n)

Answer 7:

By horizontal method:

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Question 8:

Find the product:
(x² − a²) × (x − a)

Answer 8:

By horizontal method:


i.e $(x^3+a^3)-ax(x-a)$

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Question 9:

Find the product:
(x² − y²) × (x + 2y)

Answer 9:

By horizontal method:

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Question 10:

Find the product:
(3p² + q²) × (2p² − 3q²)

Answer 10:

By horizontal method:

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Question 11:

Find the product:
(2x² − 5y²) × (x² + 3y²)

Answer 11:

By horizontal method:

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Question 12:

Find the product:
(x³ − y³) × (x² + y²)

Answer 12:

By horizontal method:

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Question 13:

Find the product:
(x⁴ + y⁴) × (x² − y²)

Answer 13:

By horizontal method:

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Question 14:

Find the product:
$\left(x^4+\frac{1}{x^4}\right)\times \left(x+\frac{1}{x}\right)$

Answer 14:

By horizontal method:

$$\begin{gathered} \left(x^4+{\displaystyle \frac{1}{x^4}}\right)\times \left(x+\frac{1}{x}\right) \\ =x^4\left(x+\frac{1}{x}\right)+\frac{1}{x^4}\left(x+\frac{1}{x}\right) \\ =x^5+x^3+\frac{1}{x^3}+\frac{1}{x^5} \\ i.e x^3(x^2+1)+\frac{1}{x^3}\left(1+{\displaystyle \frac{1}{x^2}}\right) \end{gathered}$$

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Question 15:

Find the product:
(x² − 3x + 7) × (2x + 3)

Answer 15:

By horizontal method:

$$\begin{gathered} (x^2-3x+7)\times (2x+3) \\ =2x(x^2-3x+7)+3(x^2-3x+7) \\ =2x^3-6x^2+14x+3x^2-9x+21 \\ =2x^3-3x^2+5x+21 \end{gathered}$$

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Question 16:

Find the product:
(3x² + 5x − 9) × (3x − 5)

Answer 16:

By horizontal method:
$$\begin{gathered} (3x^2+5x-9)\times (3x-5) \\ =3x(3x^2+5x-9)-5(3x^2+5x-9) \\ =9x^3+15x^2-27x-15x^2-25x+45 \\ =9x^3-52x+45 \end{gathered}$$

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Question 17:

Find the product:
(x² − xy + y²) × (x + y)

Answer 17:

By horizontal method:
$$\begin{gathered} (x^2-xy+y^2)\times (x+y) \\ =x(x^2-xy+y^2)+y(x^2-xy+y^2) \\ =x^3-x^{2}y+y^{2}x+x^{2}y-x{y}^2+y^3 \\ =x^3+y^3 \end{gathered}$$

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Question 18:

Find the product:
(x² + xy + y²) × (x − y)

Answer 18:

By horizontal method:

$$\begin{gathered} (x^2+xy+y^2)\times (x-y) \\ x(x^2+xy+y^2)-y(x^2+xy+y^2) \\ =x^3+x^{2}y+x{y}^2-x^{2}y-x{y}^2-y^3 \\ =x^3-y^3 \end{gathered}$$

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Question 19:

Find the product:
(x³ − 2x² + 5) × (4x − 1)

Answer 19:

By horizontal method:

$$\begin{gathered} (x^3-2x^2+5)\times (4x-1) \\ =4x(x^3-2x^2+5)-1(x^3-2x^2+5) \\ =4x^4-8x^3+20x-x^3+2x^2-5 \\ =4x^4-9x^3+2x^2+20x-5 \end{gathered}$$

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Question 20:

Find the product:
(9x² − x + 15) × (x² − 3)

Answer 20:

By horizontal method:

$$\begin{gathered} (9x^2-x+15)\times (x^2-3) \\ =x^2(9x^2-x+15)-3(9x^2-x+15) \\ =9x^4-x^3+15x^2-27x^2+3x-45 \\ =9x^4-x^3-12x^2+3x-45 \end{gathered}$$

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Question 21:

Find the product:
(x² − 5x + 8) × (x² + 2)

Answer 21:

By horizontal method:

$$\begin{gathered} (x^2-5x+8)\times (x^2+2) \\ =x^2(x^2-5x+8)+2(x^2-5x+8) \\ =x^4-5x^3+8x^2+2x^2-10x+16 \\ =x^4-5x^3+10x^2-10x+16 \end{gathered}$$

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Question 22:

Find the product:
(x³ − 5x² + 3x + 1) × (x² − 3)

Answer 22:

By horizontal method:

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Question 23:

Find the product:
(3x + 2y − 4) × (x − y + 2)

Answer 23:

By horizontal method:

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Question 24:

Find the product:
(x² − 5x + 8) × (x² + 2x − 3)

Answer 24:

By horizontal method:

$$\begin{gathered} (x^2-5x+8)\times (x^2+2x-3) \\ =x^2(x^2-5x+8)+2x(x^2-5x+8)-3(x^2-5x+8) \\ =x^4-5x^3+8x^2+2x^3-10x^2+16x-3x^2+15x-24 \\ =x^4-3x^3-5x^2+31x-24 \end{gathered}$$

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Question 25:

Find the product:
(2x² + 3x − 7) × (3x² − 5x + 4)

Answer 25:

By horizontal method:

$$\begin{gathered} (2x^2+3x-7)\times (3x^2-5x+4) \\ =2x^2(3x^2-5x+4)+3x(3x^2-5x+4)-7(3x^2-5x+4) \\ =6x^4-10x^3+8x^2+9x^3-15x^2+12x-21x^2+35x-28 \\ =6x^4-x^3-28x^2+47x-28 \end{gathered}$$

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Question 26:

Find the product:
(9x² − x + 15) × (x² − x − 1)

Answer 26:

By horizontal method:

$$\begin{gathered} (9x^2-x+15)\times (x^2-x-1) \\ =x^2(9x^2-x+15)-x(9x^2-x+15)-1(9x^2-x+15) \\ =9x^4-x^3+15x^2-9x^3+x^2-15x-9x^2+x-15 \\ =9x^4-10x^3+7x^2-14x-15 \end{gathered}$$