Question

Fin the squares of the following expressions:

(1) x − 3
(2) m − 8
(3) 9 − a
(4) 3x − 7
(5) 10 − 3p

Answer 1

(1) x − 3
Square of (x − 3) = (x − 3)²
The expression (x − 3)² is of the form (a − b)² .
Thus, we can use the identity (a − b)² = a² − 2ab + b² .
∴ (x − 3)² = (x)² − 2 (x) (3) + (3)²
= x² − 6x + 9

(2) m − 8
Square of (m − 8) = (m − 8)²
The expression (m − 8)² is of the form (a − b)² .
Thus, we can use the identity (a − b)² = a² − 2ab + b² .
∴ (m − 8)² = (m)² − 2 (m) (8) + (8)²
= m² − 16m + 64

(3) 9 − a
Square of (9 − a )= (9 − a)²
The expression (9 − a)² is of the form (a − b)² .
Thus, we can use the identity (a − b)² = a² − 2ab + b² .
∴ (9 − a)² = (9)² − 2 (9) (a) + (a)²
= 81 − 18a + a²

(4) 3x − 7
Square of (3x − 7) = (3x − 7)²
The expression (3x − 7)² is of the form (a − b)² .
Thus, we can use the identity (a − b)² = a² − 2ab + b² .
∴ (3x − 7)² = (3x)² − 2 (3x) (7) + (7)²
= 9x² − 42x + 49

(5) 10 − 3p
Square of 10 − 3p = (10 − 3p)²
The expression (10 − 3p)² is of the form (a − b)² .
Thus, we can use the identity (a − b)² = a² − 2ab + b² .
∴ (10 − 3p)² = (10)² − 2 (10) (3p) + (3p)²
= 100 − 60p + 9p²