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]

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Solution

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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(i)(x²− 5) (x + 5) + 25

(ii)(a²+ 5) (b³ + 3) + 5

(iii)(t + s²)(t² − s)

(iv)(a + b)(c − d) + (a − b) (c +d) + 2 (ac + bd)

(v)(x + y)(2x + y) + (x + 2y) (x − y)

(vi)(x + y)(x² − xy + y²)

(vii)(1.5x −4y) (1.5x + 4y + 3) − 4.5x + 12y

(viii)(a + b+ c) (a + b − c)

(1.5 x - 4 y) (1.5 x + 4 y + 3) - 4.5 x + 12 y

(x + y) (2 x + y) + (x + 2 y) (x - y)

(1.5 x - 4 y) (1.5 x + 4 y + 3) - 4.5 x + 12 y

(a^{2} + 5) (b^{3} + 3) + 5

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