Find the following products using appropriate identities:
$(i) (x + 3) (x + 3)$
$(ii) (x - 3) (x + 5)$
$(i) (x + 3) (x + 3)$
$(ii) (x - 3) (x + 5)$
(N/A) $(i)$ Here,we can use the identity $(x + y)^2 = x^2 + 2xy + y^2$. Substituting $y = 3$ into this identity,we get:
$(x + 3)(x + 3) = (x + 3)^2 = x^2 + 2(x)(3) + (3)^2 = x^2 + 6x + 9$.
$(ii)$ Using the identity $(x + a)(x + b) = x^2 + (a + b)x + ab$,where $a = -3$ and $b = 5$,we have:
$(x - 3)(x + 5) = x^2 + (-3 + 5)x + (-3)(5) = x^2 + 2x - 15$.
$(x + 3)(x + 3) = (x + 3)^2 = x^2 + 2(x)(3) + (3)^2 = x^2 + 6x + 9$.
$(ii)$ Using the identity $(x + a)(x + b) = x^2 + (a + b)x + ab$,where $a = -3$ and $b = 5$,we have:
$(x - 3)(x + 5) = x^2 + (-3 + 5)x + (-3)(5) = x^2 + 2x - 15$.
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