Use the identity (x + a) (x + b) = x2 + (a + b)x + ab to find the foll

1.	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» (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

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»

(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