Use suitable identities to find the following products:

(i) (x + 4) (x + 10)

(ii) (x + 8) (x - 10)

(iii) (3x + 4) (3x - 5)

(iv)

(v) (3 - 2x) (3 + 2x)

(i) (x + 4) (x + 10)

Using identity,

(x + a) (x + b) = x² + (a + b)x + ab

In (x + 4) (x + 10), a = 4 and b = 10

Now,

(x + 4) (x + 10) = x² + (4 + 10)x + (4 * 10)

= x² + 14x + 40

(ii) (x + 8) (x - 10)

Using identity,

(x + a) (x + b) = x² + (a + b) x + ab

Here, a = 8 and b = -10

(x + 8) (x – 10) = x² + {8 + (-10)} x + {8 * (-10)}

= x² + (8 – 10)x – 80

= x² – 2x – 80

(iii) (3x + 4) (3x - 5)

Using identity,

(x + a) (x + b) = x² + (a + b) x + ab

Here, x = 3x, a = 4 and b = -5

(3x + 4) (3x – 5) = (3x)² + {4 + (-5)} 3x + {4 * (-5)}

= 9x² + 3x (4 – 5) – 20

= 9x² – 3x – 20

(iv)

Using identity,

(x + y) (x – y) = x² – y²

Here, x = y² and y = 3/2

(v) (3 - 2x) (3 + 2x)

Using identity,

(x + y) (x – y) = x² – y²

Here, x = 3 and y = 2x

(3 – 2x) (3 + 2x) = 3² – (2x)²

= 9 – 4x²