### Question 1. Find the following products:

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

**Solution:**

By simplifying the given expression, we get

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

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