Question

Find each of the following products:

(i) (x + 3)(x – 3) 

(ii) (2x + 5)(2x – 5) 

(iii) (8 + x)(8 – x) 

(iv) (7x + 11y)(7x – 11y)

Answer 1

(i) Given, 

(x + 3)(x – 3) 

By using the formula (a + b) (a – b) = a² – b² 

We get; 

= x(x + 3) – 3(x + 3) 

= x² + 3x – 3x – 9 

= x² – 9

(ii) Given, 

(2x + 5)(2x – 5) 

By using the formula (a + b) (a – b) = a² – b² 

We get; 

= 2x(2x + 5) – 5(2x + 5) 

= 4x² + 10x – 10x – 25 

= 4x² – 25

(iii) Given, 

(8 + x)(8 – x) 

By using the formula (a + b) (a – b) = a² – b² 

We get; 

= 8(8 + x) – x(8 + x) 

= 64 + 8x – 8x – x² 

= 64 – x²

(iv) Given, 

(7x + 11y)(7x – 11y) 

By using the formula (a + b) (a – b) = a² – b² 

We get; 

= 7x(7x + 11y) – 11y(7x + 11y) 

= 49x² + 77xy – 77xy – 121y² 

= 49x² – 121y²