Find the following products using appropriate identities :
$(i) $ $ (x + 3) (x + 3)$
$(ii)$ $(x -3) (x + 5)$
Find the following products using appropriate identities :
$(i) $ $ (x + 3) (x + 3)$
$(ii)$ $(x -3) (x + 5)$
$(i)$ Here we can use Identity $I :(x+y)^{2}=x^{2}+2 x y+y^{2} .$ Putting $y=3$ in it,
we get $(x+3)(x+3)=(x+3)^{2}=x^{2}+2(x)(3)+(3)^{2}$
$=x^{2}+6 x+9$
$(ii)$ Using Identity $IV$ above, i.e., $(x+a)(x+b)=x^{2}+(a+b) x+a b,$ we have
$(x-3)(x+5) =x^{2}+(-3+5) x+(-3)(5)$
$=x^{2}+2 x-15$
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