Question

(1) Expand the following using formulas:

(i) (5 + m)²
(ii) (11 − 2x)²
(iii) (7 − 3y)³
(iv) (6 − 5q) (6 + 5q)
(v) (10 − 3b) (10 + 3b)

Answer 1

(i) (5 + m)²
The given expression is of the form (a + b)² .
Thus, we can use the identity (a + b)² = a² + 2ab + b² .
∴ (5 + m)² = (5)² + 2 (5) (m) + (m)²
= 25 + 10m + m²

(ii) (11 − 2x)²
The given expression is of the form (a − b)² .
Thus, we can use the identity (a − b)² = a² − 2ab + b² .
∴ (11 − 2x)² = (11)² − 2 (11) (2x) + (2x)²
= 121 − 44x + 4x²

(iii) (7 − 3y)²
The given expression is of the form (a − b)² .
Thus, we can use the identity (a − b)² = a² − 2ab + b² .
∴ (7 − 3y)² = (7)² − 2 (7) (3y) + (3y)²
= 49 − 42y + 9y²

(iv) (6 − 5q) (6 + 5q)
The given expression is of the form (a + b) (a − b).
Thus, we can use the identity (a + b) (a − b) = a² − b² .
∴ (6 − 5q) (6 + 5q) = (6)² − (5q)²
= 36 − 25q²

(v) (10 − 3b) (10 + 3b)
The given expression is of the form (a + b) (a − b).
Thus, we can use the identity (a + b) (a − b) = a² − b² .
∴ (10 − 3b) (10 + 3b)= (10)² − (3b)²
= 100 − 9b²