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

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 6D.

**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

**Question 1.**

**Solution:**

(i)(x + 6)(x + 6)

= (x + 6)^{2}

You can also Download **NCERT Solutions for Class 8 English** to help you to revise complete Syllabus and score more marks in your examinations.

**Question 2.**

**Solution:**

(i) (x – 4)(x – 4)

= (x – 4)^{2}

**Question 3.**

**Solution:**

(i)(8a + 3b)^{2}

= (8a)^{2} + 2 x 8a x 3b + (3b)^{2}

**Question 4.**

**Solution:**

(i)(x + 3)(x – 3)

= (x)^{2} – (3)^{2}

**Question 5.**

**Solution:**

(i) (54)^{2}

= (50 + 4)^{2}

**Question 6.**

**Solution:**

(i) (69)^{2}

= (70 – 1)^{2}

**Question 7.**

**Solution:**

(i)(82)^{2} – (18)^{2}

= (82 – 18)(82 – 18)

**Question 8.**

**Solution:**

9x^{2} + 24x + 16

= (3x)^{2} + 2 x 3x x 4 + (4)^{2}

= (3x + 4)^{2}

= (3 x 12 + 4)^{2}

= (36 + 4)^{2}

= (40)^{2}

= 1600 Ans.

**Question 9.**

**Solution:**

64x^{2} + 81y^{2} + 144xy = (8x)^{2} + (9y)^{2} + 2 x 8x x 9y

= (8x + 9y)^{2}

= \({ \left( 8\times 11+9\times \frac { 4 }{ 3 } \right) }^{ 2 }\)

= (88 + 12)^{2}

= (100)^{2}

= 10000 Ans.

**Question 10.**

**Solution:**

(36x^{2} + 25y^{2} – 60xy)

= (6x)^{2} + (5y)^{2} – 2 x 6x x 5y

= (6x – 5y)^{2}

= \({ \left( 6\times \frac { 2 }{ 3 } -5\times \frac { 1 }{ 5 } \right) }^{ 2 } \)

= (4 – 1)^{2}

= (3)^{2} = 9

**Question 11.**

**Solution:**

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

Squaring on both sides

**Question 12.**

**Solution:**

\(\left( x-\frac { 1 }{ x } \right) =5 \)

(i) Squaring on both sides

**Question 13.**

**Solution:**

(i) (x + 1) (x – 1) (x^{2} + 1)

= {(x)^{2} – (1)^{2}} (x^{2} + 1)

= (x^{2} – 1) (x^{2} + 1)

= (x^{2})^{2} – (1)^{2} = x^{4} – 1 Ans.

(ii) (x – 3) (x + 3) (x^{2} + 9)

= {(x)^{2} – (3)^{2} } (x^{2} + 9)

= (x^{2} – 9) (x^{2} + 9)

= (x^{2})^{2} – (9)^{2} = x^{4} – 81 Ans.

(iii) (3x – 2y) (3x + 2y) (9x^{2} + 4y^{2})

= {(3x)^{2} – (2y)^{2}} (9x^{2} + 4y^{2})

= (9x^{2} – 4y^{2}) (9x^{2} + 4y^{2})

= (9x^{2})^{2} – (4y^{2})^{2}

= 81x^{4} – 16y^{4} Ans.

(iv) (2p + 3) (2p – 3) (4p^{2} + 9)

= {(2p)^{2} – (3)^{2}} (4p^{2} + 9)

= (4p^{2} – 9) (4p^{2} + 9)

= (4p^{2})^{2} – (9)^{2} = 16p^{4} – 81 Ans.

**Question 14.**

**Solution:**

x + y = 12

Squaring both sides,

(x + y)^{2} = (12)^{2}

=> x^{2} + y^{2} + 2xy = 144

=> x^{2} + y^{2} + 2 x 14 = 144

=> x^{2} + y^{2} + 28 = 144

=> x^{2} + y^{2} = 144 – 28 = 116

x^{2} + y^{2} = 116 Ans.

**Question 15.**

**Solution:**

x – y = 7

Squaring both sides,

(x – y)^{2} = (7)^{2}

=> x^{2} + y^{2} – 2xy = 49

=> x^{2} + y^{2} – 2 x 9 = 49

=> x^{2} + y^{2} – 18 = 49

=> x^{2} + y^{2} = 49 + 18 = 67

x^{2} + y^{2} = 67 Ans.

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

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