Question

Use a suitable identity to get each of the following products.

(i) (x + 3) (x + 3) (ii) (2y + 5) (2y + 5)

(iii) (2a ­− 7) (2a − 7) (iv)

(v) (1.1m − 0.4) (1.1 m + 0.4) (vi) (a² + b²) (− a² + b²)

(vii) (6x − 7) (6x + 7) (viii) (− a + c) (− a + c)

(ix) (x) (7a − 9b) (7a − 9b)

Answer 1

The products will be as follows.

(i) (x + 3) (x + 3) = (x + 3)²

= (x)² + 2(x) (3) + (3)² [(a + b)² = a² + 2ab + b²]

= x² + 6x + 9

(ii) (2y + 5) (2y + 5) = (2y + 5)²

= (2y)² + 2(2y) (5) + (5)² [(a + b)² = a² + 2ab + b²]

= 4y² + 20y + 25

(iii) (2a ­− 7) (2a − 7) = (2a − 7)²

= (2a)² − 2(2a) (7) + (7)² [(a − b)² = a² − 2ab + b²]

= 4a² − 28a + 49

(iv)

[(a − b)² = a² − 2ab + b²]

(v) (1.1m − 0.4) (1.1 m + 0.4)

= (1.1m)² − (0.4)² [(a + b) (a − b) = a² − b²]

= 1.21m² − 0.16

(vi) (a² + b²) (− a² + b²) = (b² + a²) (b² − a²)

= (b²)² − (a²)² [(a + b) (a − b) = a² − b²]

= b⁴ − a⁴

(vii) (6x − 7) (6x + 7) = (6x)² − (7)² [(a + b) (a − b) = a² − b²]

= 36x² − 49

(viii) (− a + c) (− a + c) = (− a + c)²

= (− a)² + 2(− a) (c) + (c)² [(a + b)² = a² + 2ab + b²]

= a² − 2ac + c²

(ix)

[(a + b)² = a² + 2ab + b²]

(x) (7a − 9b) (7a − 9b) = (7a − 9b)²

= (7a)² − 2(7a)(9b) + (9b)² [(a − b)² = a² − 2ab + b²]

= 49a² − 126ab + 81b²