Question

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

(i) (2x +5y) (2x + 3y) 

(ii) (2a² +9) (2a² + 5)

(iii) (xyz − 4) (xyz − 2)

Answer 1

(i) (2x +5y) (2x + 3y) 

= (2x)² + (5y + 3y) (2x) + (5y) (3y)

= 4x² + 16xy + 15y²

(ii) (2a² +9) (2a² + 5) 

= (2a²)² + (9 + 5) (2a²) + (9) (5)

= 4a⁴ + 28a² + 45

(vii) (xyz − 4) (xyz − 2)

+ (xyz)² + [ (-4) + (-2) ] (xyz) + (-4) (-2)

= x²y²z² - 6xyz + 8