1.Use suitable identities to find the following products :
i)$$(x + 4)(x + 10)$$
ii)$$(x + 8)(x - 10)$$
iii)$$(3x - 4)(3x - 5)$$
iv)$$(y^2 + 3/2)(y^2 - 3/2)$$
v)$$(3 - 2x)(3 + 2x)$$

i)$$(x + 4)(x + 10)$$
Using identity (iv), i.e.,$$(x + a)(x + b) = x^2 + (a + b)x + ab$$
We have, $$(x + 4)(x + 10) = x^2 + (4 + 10)x + (4)(10)$$
$$= x^2 + 14x + 40$$

ii)$$(x + 8)(x - 10)$$
Using identity (iv), i.e.,$$(x + a)(x + b) = x^2 + (a + b)x + ab$$
We have, $$(x + 8)(x - 10) = x^2 + (8 - 10)x + (8)(-10)$$
$$= x^2 - 2x - 80$$

iii)$$(3x + 4)(3x - 5)$$
Using identity (iv), i.e.,$$(x + a)(x + b) = x^2 + (a + b)x + ab$$
We have, $$(3x + 4)(3x - 5) = (3x)^2 + (4 - 5)x + (4)(5)$$
$$= 9x^2 - x + 20$$

iv)$$(y^2 + 3/2)(y^2 - 3/2)$$
Using identity (iii), i.e.,$$(a^2 - b^2) = (a + b)(a - b)$$
We have, $$(y^2 + 3/2)(y^2 - 3/2) = (y^2)^2 - (3/2)^2$$
$$= y^4 - 9/4$$

v)$$(3 - 2x)(3 + 2x)$$
Using identity (iii), i.e.,$$(a^2 - b^2) = (a + b)(a - b)$$
We have, $$(3 - 2x)(3 + 2x) = (3)^2 - (2x)^2)$$
$$= 9 - 4x^2$$