# Class 8 RD Sharma Solutions – Chapter 6 Algebraic Expressions And Identities – Exercise 6.7

### Question 1. Find the following products:

### (i) (x + 4) (x + 7)

**Solution:**

By simplifying the given expression, we get

Attention reader! All those who say programming isn't for kids, just haven't met the right mentors yet. Join the

Demo Class for First Step to Coding Course,specificallydesigned for students of class 8 to 12.The students will get to learn more about the world of programming in these

free classeswhich will definitely help them in making a wise career choice in the future.x (x + 7) + 4 (x + 7)

x

^{2}+ 7x + 4x + 28x

^{2}+ 11x + 28

### (ii) (x – 11) (x + 4)

**Solution:**

By simplifying the given expression, we get

x (x + 4) – 11 (x + 4)

x

^{2}+ 4x – 11x – 44x

^{2}– 7x – 44

### (iii) (x + 7) (x – 5)

**Solution:**

By simplifying the given expression, we get

x (x – 5) + 7 (x – 5)

x

^{2}– 5x + 7x – 35x

^{2}+ 2x – 35

### (iv) (x – 3) (x – 2)

**Solution:**

By simplifying the given expression, we get

x (x – 2) – 3 (x – 2)

x

^{2}– 2x – 3x + 6x

^{2}– 5x + 6

### (v) (y^{2} – 4) (y^{2} – 3)

**Solution:**

By simplifying the given expression, we get

y

^{2}(y^{2}– 3) – 4 (y^{2}– 3)y

^{4}– 3y^{2}– 4y^{2}+ 12y

^{4}– 7y^{2}+ 12

### (vi) (x + 4/3) (x + 3/4)

**Solution:**

By simplifying the given expression, we get

x (x + 3/4) + 4/3 (x + 3/4)

x

^{2}+ 3x/4 + 4x/3 + 12/12x

^{2}+ 3x/4 + 4x/3 + 1x

^{2}+ 25x/12 + 1

### (vii) (3x + 5) (3x + 11)

**Solution:**

By simplifying the given expression, we get

3x (3x + 11) + 5 (3x + 11)

9x

^{2}+ 33x + 15x + 559x

^{2}+ 48x + 55

### (viii) (2x^{2} – 3) (2x^{2}+ 5)

**Solution:**

By simplifying the given expression, we get

2x

^{2}(2x^{2}+ 5) – 3 (2x^{2}+ 5)4x

^{4}+ 10x^{2}– 6x^{2}– 154x

^{4}+ 4x^{2}– 15

### (ix) (z^{2} + 2) (z^{2}– 3)

**Solution:**

By simplifying the given expression, we get

z

^{2}(z^{2}– 3) + 2 (z^{2}– 3)z

^{4}– 3z^{2}+ 2z^{2}– 6z

^{4}– z^{2}– 6

### (x) (3x – 4y) (2x – 4y)

**Solution:**

By simplifying the given expression, we get

3x (2x – 4y) – 4y (2x – 4y)

6x

^{2}– 12xy – 8xy + 16y^{2}6x

^{2}– 20xy + 16y^{2}

### (xi) (3x^{2} – 4xy) (3x^{2} – 3xy)

**Solution:**

By simplifying the given expression, we get

3x

^{2}(3x^{2}– 3xy) – 4xy (3x^{2}– 3xy)9x

^{4}– 9x^{3}y – 12x^{3}y + 12x^{2}y^{2}9x

^{4}– 21x^{3}y + 12x^{2}y^{2}

### (xii) (x + 1/5) (x + 5)

**Solution:**

By simplifying the given expression, we get

x (x + 1/5) + 5 (x + 1/5)

x

^{2}+ x/5 + 5x + 1x

^{2}+ 26/5x + 1

### (xiii) (z + 3/4) (z + 4/3)

**Solution:**

By simplifying the given expression, we get

z (z + 4/3) + 3/4 (z + 4/3)

z

^{2}+ 4/3z + 3/4z + 12/12z

^{2}+ 4/3z + 3/4z + 1z

^{2}+ 25/12z + 1

### (xiv) (x^{2}+ 4) (x^{2} + 9)

**Solution:**

By simplifying the given expression, we get

x

^{2}(x^{2}+ 9) + 4 (x^{2}+ 9)x

^{4}+ 9x^{2}+ 4x^{2}+ 36x

^{4}+ 13x^{2}+ 36

### (xv) (y^{2} + 12) (y^{2}+ 6)

**Solution:**

By simplifying the given expression, we get

y

^{2}(y^{2}+ 6) + 12 (y^{2}+ 6)y

^{4}+ 6y^{2}+ 12y^{2}+ 72y

^{4}+ 18y^{2}+ 72

### (xvi) (y^{2} + 5/7) (y^{2} – 14/5)

**Solution:**

By simplifying the given expression, we get

y

^{2}(y^{2}– 14/5) + 5/7 (y^{2}– 14/5)y

^{4}– 14/5y^{2}+ 5/7y^{2}– 2y

^{4}– 73/35y^{2}– 2

### (xvii) (p^{2} + 16) (p^{2} – 1/4)

**Solution:**

By simplifying the given expression, we get

p

^{2}(p^{2}– 1/4) + 16 (p^{2}– 1/4)p

^{4}– 1/4p^{2 }+ 16p^{2}– 4p

^{4}+ 63/4p^{2}– 4

### Question 2. Evaluate the following:

### (i) 102 × 106

**Solution:**

By simplifying the given expression, we get

102 × 106 = (100 + 2) (100 + 6)

= 100 (100 + 6) + 2 (100 + 6)

= 10000 + 600 + 200 + 12

= 10812

### (ii) 109 × 107

**Solution:**

By simplifying the given expression, we get

109 × 107 = (100 + 9) (100 + 7)

= 100 (100 + 7) + 9 (100 + 7)

= 10000 + 700 + 900 + 63

= 11663

### (iii) 35 × 37

**Solution:**

By simplifying the given expression, we get

35 × 37 = (30 + 5) (30 + 7)

= 30 (30 + 7) + 5 (30 + 7)

= 900 + 210 + 150 + 35

= 1295

### (iv) 53 × 55

**Solution:**

By simplifying the given expression, we get

53 × 55 = (50 + 3) (50 + 5)

= 50 (50 + 5) + 3 (50 + 5)

= 2500 + 250 + 150 + 15

= 2915

### (v) 103 × 96

**Solution:**

By simplifying the given expression, we get

103 × 96 = (100 + 3) (100 – 4)

= 100 (100 – 4) + 3 (100 – 4)

= 10000 – 400 + 300 – 12

= 10000 – 112

= 9888

### (vi) 34 × 36

**Solution:**

By simplifying the given expression, we get

34 × 36 = (30 + 4) (30 + 6)

= 30 (30 + 6) + 4 (30 + 6)

= 900 + 180 + 120 + 24

= 1224

### (vii) 994 × 1006

**Solution:**

By simplifying the given expression, we get

994 × 1006 = (1000 – 6) (1000 + 6)

= 1000 (1000 + 6) – 6 (1000 + 6)

= 1000000 + 6000 – 6000 – 36

= 999964