Question 1.

Expand :

i. (a + 2)(a – 1)

ii. (m – 4)(m + 6)

iii. (p + 8) (p – 3)

iv. (13 + x)(13 – x)

v. (3x + 4y) (3x + 5y)

vi. (9x – 5t) (9x + 3t)

Solution:

i. (a + 2)(a – 1)

= a² + (2 – 1) a + 2 × (-1)

..[∵ (x + A) (x + B) = x² + (A + B)x + AB]

= a² + a – 2

ii. (m – 4)(m + 6)

= m² + (- 4 + 6) m + (-4) × 6

…[∵ (x + a) (x + b) = x² + (a + b)x + ab]

= m² + 2m – 24

iii. (p + 8) (p – 3)

= p² + (8 – 3) p + 8 x (-3)

…[∵ (x + a) (x + b) = x² + (a + b)x + ab]

= p² + 5p – 24

iv. (13 + x) (13 – x)

= (13)² + (x – x) 13 + x × (-x)

…[∵ (x + a) (x + b) = x² + (a + b)x + ab]

= 169 + 0 × 13 – x²

= 169 – x²

v. (3x + 4y) (3x + 5y)

= (3x)² + (4y + 5y) 3x + 4y × 5y

…[∵ (x + a) (x + b) = x² + (a + b)x + ab]

= 9x² + 9y × 3x + 20y²

= 9x² + 27xy + 20y²

vi. (9x – 5t) (9x + 3t)

= (9x)² + [(-5t) + 3t] 9x + (-5t) × 3t

…[∵ (x + a) (x + b) = x² + (a + b)x + ab]

= 81x² + (-2t) × 9x – 15t²

= 81x² – 18xt – 15t²

**Intext Questions and Activities**

Question 1.

Use the above formulae to fill proper terms in the following boxes. (Textbook pg. no. 23)

- (x + 2y)² = x² + ___ + 4y²
- (2x – 5y)² = __ – 20xy + __
- (101)² = (100 + 1)² = ___+ ___ + 1² = ___
- (98)² = (100 – 2)² = 10000 – ___ + ___ = ___
- (5m + 3n) (5m – 3n) = ___ – ___ = ___ – ___

Solution:

- (x + 2y)² = x² + 4xy + 4y²
- (2x – 5y)² = 4x² – 20xy + 25y²
- (101)² = (100 + 1)² = 10000 + 200 + 1² = 10201
- (98)² = (100 – 2)² = 10000 – 400 + 4 = 9604
- (5m + 3n) (5m – 3n) = (5m)² – (3n)² = 25m² – 9n²

Question 2.

Expand (x + a) (x + b) using formulae for areas of a square and a rectangle. (Textbook pg. no. 23)

(x + a) (x + b) = x² + ax + bx + ab

(x + a) (x + b) = x² + (a + b) x + ab

Solution:

∴ (x + a) (x + b) = x² + ax + bx + ab

∴ (x + a) (x + b) = x² + (a + b) x + ab