Question

Use the identity (x + a) (x + b) = x² + (a + b)x + ab to find the following products. 

(i) (x + 3) (x + 7) (ii) (4x +5) (4x + 1)

(iii) (4x − 5) (4x − 1) (iv) (4x + 5) (4x − 1)

Answer 1

(i) (x + 3) (x + 7) 

= x² + (3 + 7) x + (3) (7) 

= x² + 10x + 21

(ii) (4x + 5) (4x + 1) 

= (4x)² + (5 + 1) (4x) + (5) (1) 

= 16x² + 24x + 5

(iii) (4x - 5) (4x - 1)

= (4x)² + [ (-5) + (-1) ] (4x) + (5) (-1)

= 16x² + 16x -5

(iv) (4x + 5) (4x - 1) 

= (4x)² + [ (5) + (-1) ] (4x) + (5) (-1)

=16x² + 16x − 5