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#### Question O2:

How do we represent a ‘Universal set’ through Venn diagram.

A universal set is represented by a rectangle.

#### Question O1:

What is the expansion of (x + a) (x + b)

The expansion of.

#### Question O2:

Express 12 × 14 in the form of (x + a) (x + b)

The term can be expressed in the form of as .

#### Question O3:

Name the constant in the product of (m2 + 4) (m2 + 5)

In, we have. Thus, the constant in the product of these is.

#### Question W1:

Find the product using the formula.

(1) (x + 3) (x + 7)

Using the identity (x + a) (x + b) = x2 + (a + b) x + ab:

(x + 3) (x + 7) = x2 + (3 + 7) x + 21

= x2 + 10 x + 21

(2) (y + 3) (y + 5)

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

(y + 3) (y + 5) = y2 + (3 + 5) x + 15

= y2 + 8 y + 15

(3) (m + 4) (m + 5)

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

(m + 4) (m + 5) = m2 + (4 + 5) m + 20

= m2 + 9 m + 20

(4) (a + 10) (a + 5)

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

(a + 10) (a + 5) = a2 + (10 + 5) a + 20

= m2 + 15 m + 20

(5) (x + 8) (x + 2)

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

(x + 8) (x + 2) = x2 + (8 + 2) x + 16

= x2 + 10 x + 16

(6) (2a + 3) (2a − 7)

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

(2a + 3) (2a − 7) = 4a2 + (3 − 7) 2a − 21

= 4a2 − 8a − 21

(7) (2x − 5) (2x + 3)

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

(2x − 5) (2x + 3) = 4x2 + (−5 + 3) 2x − 15

= 4x2 − 4 x − 15

(8) (3x − 4) (3x + 8)

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

(3x − 4) (3x + 8) = (3x)2 + (−4 + 8) 3x + (−4) × 8

= 9x2 + 12 x − 32

(9) (a2 − 3) (a2 − 5)

Using the identity (x + a) (x + b) = x2 + (a + b) x + ab:

(a2 − 3) (a2 − 5) = a4 + (−3 − 5) a2 + (−3) × (−5)

= a4 − 8a2 + 15

(10) (3p2 + 1) (3p2 + 4)

Using the identity (x + a) (x + b) = x2 + (a + b) x + ab:

(3p2 + 1) (3p2 + 4) = (3p)4 + (1 + 4) 3p2 + 1 × 4

= 9p4 + 15p2 + 4

#### Question W2:

Find the product of the following numbers using the formula (x + a) (x + b).

(1) 105 × 108

Using the identity (x + a) (x + b) = x2 + (a + b) x + ab;

105 × 108 = (100 + 5) (100 + 8)

= (100)2 + (5 + 8) × 100 + 5 × 8

= 10000 + 1300 + 40

= 11340

(2) 130 × 98

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

130 × 98 = (100 + 30) (100 − 2)

= 10000 + (30 − 2) × 100 + 30 × (−2)

= 10000 + 2800 − 60

= 12740

(3) 104 × 94

Using the identity (x + a) (x + b) = x2 + (a + b) x + ab:

104 × 94 = (100 + 4) (100 − 6)

= 10000 + (4 − 6) × 100 + 4 × (−6)

= 10000 − 200 − 24

= 9776

(4) 99 × 97

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

99 × 97 = (100 − 1) (100 − 3)

= 10000 + (−1 − 3)×100 + 3

= 10000 − 400 + 3

= 9603

(5) 112 × 90

Using the identity (x + a) (x + b) = x2 + (a + b) x + a b:

112 × 90 = (100 + 12) (100 − 10)

= 10000 + (12 − 10) × 100 + 12 × (−10)

= 10000 + 200 − 120

= 10080

#### Question O1:

What is the expanded form of (a + b)2

The expanded form of is .

#### Question W1:

Expand by using a suitable formula.

(1) Using the identity (a + b)2 = a2 + 2ab + b2:

(2) Using the identity (a + b)2 = a2 + 2ab + b2:

(3) Using the identity (a + b)2 = a2 + 2ab + b2:

(4) Using the identity (a + b)2 = a2 + 2ab + b2:

(5) Using the identity (a + b)2 = a2 + 2ab + b2:

(6) Using the identity (a + b)2 = a2 + 2ab + b2:

(7) Using the identity (a + b)2 = a2 + 2ab + b2:

(8) Using the identity (a + b)2 = a2 + 2ab + b2:

(9) Using the identity (a + b)2 = a2 + 2ab + b2:

(10) Using the identity (a + b)2 = a2 + 2ab + b2:

#### Question O2:

Express (12)2 in the form of (a + b)2

(12)2 can be expressed as .

#### Question W2:

Find the squares of the following numbers using the formula.

(a + b)2 = a2 + 2ab + b2

(1)

(2)

(3)

(4)

(5)

#### Question W3.2:

The length of each side of a square land shown in the figure is (a + b) units. In the corner of this land there is a square portion of length ‘b’ units is useless. Find the area of the portion of the land which is useful.

Total area of the square land = (a + b)2 = a2 + 2ab + b2

Area of useless land = b2

∴ Useful land = a2 + 2ab + b2b2 = (a2 + 2ab) sq units

#### Question W3.1:

Find the area of a square having its side (3x + 2y) using the formula.

Side = 3 x + 2 y

Using the identity (a + b)2 = a2 + 2ab + b2:

Expand (m + 2)2

=

#### Question W4.1:

Fill up the blanks.

#### Question W4.2:

Fill up the blanks.

#### Question W4.3:

Fill up the blanks.

#### Question W1:

Use the formula and expand the following:

(1) Using the identity (ab)2 = a2 − 2ab + b2:

(2) Using the identity (ab)2 = a2 − 2ab + b2:

(3) Using the identity (ab)2 = a2 − 2ab + b2:

(4) Using the identity (ab)2 = a2 − 2ab + b2:

(5) Using the identity (ab)2 = a2 − 2ab + b2:

(6) Using the identity (ab)2 = a2 − 2ab + b2:

(7) Using the identity (ab)2 = a2 − 2ab + b2:

(8) Using the identity (ab)2 = a2 − 2ab + b2:

(9) Using the identity (ab)2 = a2 − 2ab + b2:

(10) Using the identity (ab)2 = a2 − 2ab + b2:

#### Question O1:

Expand (ab)2

The expansion of .

#### Question O2:

Express (8)2 in the form of (ab)2

(8)2 can be expressed in the form of , as .

#### Question W2:

Find the square of the following numbers using the formula:

(ab)2 = a2 − 2ab + b2

(1)

(2)

(3)

(4)

(5)

#### Question O3:

Expand (p − 3)2

The expansion of is .

#### Question W3.1:

Fill in the blanks with appropriate answers:

Using the identity (ab)2 = a2 − 2ab + b2:

#### Question W3.2:

Fill in the blanks with appropriate answers:

Using the identity (ab)2 = a2 − 2ab + b2:

#### Question W3.3:

Fill in the blanks with appropriate answers:

Using the identity (ab)2 = a2 − 2ab + b2:

Therefore, the missing terms are 24ab, 4a and 3b

#### Question W3.4:

Fill in the blanks with appropriate answers:

Using the identity (ab)2 = a2 − 2ab + b2:

#### Question W3.5:

Fill in the blanks with appropriate answers:

Using the identity (ab)2 = a2 − 2ab + b2:

#### Question O1:

What is the expanded form of (a + b) (ab).

The expanded form of is .

#### Question O2:

Find the product of (p + 4) (p − 4).

#### Question O3:

Expand 12 × 8 by using the formula (a + b) (ab).

#### Question W1:

Use the formula and find the product:

 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

(1) Using the identity (a + b) (ab) = a2b2:

(2) Using the identity (a + b) (ab) = a2b2:

(3) Using the identity (a + b) (ab) = a2b2:

(4) Using the identity (a + b) (ab) = a2b2:

(5) Using the identity (a + b) (ab) = a2b2:

(6) Using the identity (a + b) (ab) = a2b2;

(7) Using the identity (a + b) (ab) = a2b2:

(8) Using the identity (a + b) (ab) = a2b2:

(9) Using the identity (a + b) (ab) = a2b2:

(10) Using the identity (a + b) (ab) = a2b2:

#### Question W2:

Use the formula and find the product:

(1) Using the identity (a + b) (ab) = a2b2:

(2) Using the identity (a + b) (ab) = a2b2:

(3) Using the identity (a + b) (ab) = a2b2:

#### Question W3:

Match the following:

 A B 1) (m + 2n) (m − 2n) a) m2 − 16 2) (3m + n) (3m − n) b) 4m2 − 25n2 3) (m + 4) (m − 4) c) 4m2 + 25n2 4) (2m + 5n) (2m − 5n) d) m2 − 4n2 e) 9m2 + n2 f) 9m2 − n2

Using the identity (a + b) (ab) = a2b2:

(1)

(2)

(3)

(4)

Hence, the match is (1) − (d), (2) − (f), (3) − (a) and (4) − (b)

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