Question

Evaluate:

(i) (a + b)(a - b)

(ii) (a² + b²)(a + b)(a - b); using the result of (i).

(iii) (a⁴ + b⁴)(a² + b²)(a + b)(a - b); using the result of (ii).

Answer 1

(i) (a + b)(a - b)

= a (a - b) + b(a - b)

= a² - ab + ab - b² 

= a² - b² 

(ii) (a² + b²)(a + b)(a - b)

= (a² + b²)(a² - b²)    ...{from(i)}

= a2 (a² - b²) + b² (a² - b²) 

= a⁴ - a²b² + a²b² - b⁴ 

= a⁸ - a⁴b⁴ + a⁴b⁴ - b⁸

= a⁴ - b⁴ 

(iii) (a⁴ + b⁴)(a² + b²)(a + b)(a - b)

= (a⁴ + b⁴) (a⁴ - b⁴)  ....{from(ii)}

= a⁴ (a⁴ + b⁴) + b⁴ (a⁴ + b⁴) 

= a⁸ - a⁴b⁴ + a⁴b⁴ - b⁸

= a⁸ - b⁸