Simplify the following: (i) (1.5x−4y)(1.5x+4y+3) (ii) (x+y)

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Simplify the following:
$(i) (1.5 x - 4 y) (1.5 x + 4 y + 3)$
$(i i) (x + y) (2 x + y) + (x + 2 y) (x - y)$
$(i i i) (a^{2} + 5) (b^{3} + 3) + 5$ [3 MARKS]

Options:

Answer: Option A
:

Application: 1 Mark each
$(i) (1.5 x - 4 y) (1.5 x + 4 y + 3)$
$2.25 x^{2} + 6 x y + 4.5 x - 6 x y - 16 y^{2} - 12 y$
$\Rightarrow 2.25 x^{2} - 16 y^{2} + 4.5 x - 12 y$
$(i i) (x + y) (2 x + y) + (x + 2 y) (x - y)$
$(2 x^{2} + x y + 2 x y + y^{2}) + (x^{2} + x y - 2 y^{2})$
$3 x^{2} + 4 x y - y^{2}$
$(i i i) (a^{2} + 5) (b^{3} + 3) + 5$
$a^{2} b^{3} + 3 a^{2} + 5 b^{3} + 15 + 5$
$\Rightarrow a^{2} b^{3} + 3 a^{2} + 5 b^{3} + 20$

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