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# Use suitable identities to find the following products :i)$$(x + 4)(x + 10)$$ii)$$(x + 8)(x - 10)$$iii)$$(3x - 4)(3x - 5)$$iv)$$(y^2 + \frac{3}{2} )(y^2 - \frac{3}{2} )$$v)$$(3 - 2x)(3 + 2x)$$

i)$$(x + 4)(x + 10)$$
$$[\because (x + a)(x + b) = x^2 + (a + b)x + ab]$$

We have,
$$=(x + 4)(x + 10)$$
$$= x^2 + (4 + 10)x + (4)(10)$$
$$= x^2 + 14x + 40$$

ii) $$(x + 8)(x - 10)$$
$$[\because (x + a)(x + b) = x^2 + (a + b)x + ab]$$
We have,
$$= (x + 8)(x - 10)$$
$$= x^2 + (8 - 10)x + (8)(-10)$$
$$= x^2 - 2x - 80$$

iii) $$(3x + 4)(3x - 5)$$
$$[\because (x + a)(x + b) = x^2 + (a + b)x + ab]$$
We have,
$$(3x + 4)(3x - 5)$$
$$= (3x)^2 + (4 - 5)x + (4)(5)$$
$$= 9x^2 - x + 20$$

iv) $$(y^2 + \frac{3}{2} )(y^2 - \frac{3}{2} )$$
$$[\because (a^2 - b^2) = (a + b)(a - b)]$$
We have,
$$(y^2 + \frac{3}{2} )(y^2 - \frac{3}{2} )$$
$$= (y^2)^2 - (\frac{3}{2} )^2$$
$$= y^4 - \frac{9}{4}$$

v) $$(3 - 2x)(3 + 2x)$$
$$[\because (a^2 - b^2) = (a + b)(a - b)]$$
We have,
$$(3 - 2x)(3 + 2x)$$
$$= (3)^2 - (2x)^2)$$
$$= 9 - 4x^2$$