Simplify: $(3 a - 5 b)^{3} - (3 a + 5 b)^{3}$

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Solution

$(3 a - 5 b)^{3} - (3 a + 5 b)^{3}$
Using, $(a^{3} - b^{3}) = (a - b) (a^{2} + a b + b^{2})$
$= (3 a - 5 b - 3 a - 5 b) [(3 a - 5 b)^{2} + (3 a + 5 b)^{2} + (3 a - 5 b) (3 a + 5 b)]$
$= (- 10 b) [9 a^{2} - 2 \times 3 a \times 5 b + 25 b^{2} + 9 a^{2} + 2 \times 3 a \times 5 b + 25 b^{2} + 9 a^{2} - 25 b^{2}]$
$= (- 10 b) [9 a^{2} + 25 b^{2} + 9 a^{2} + 9 a^{2}]$
$= (- 10 b) (27 a^{2} + 25 b^{2})$

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

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$(i) (1.5 x - 4 y) (1.5 x + 4 y + 3)$

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$(i i i) (a^{2} + 5) (b^{3} + 3) + 5$ [3 MARKS]

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Simplify: (3a−5b)3−(3a+5b)3

(3a−5b)3−(3a+5b)3Using,(a3−b3)=(a−b)(a2+ab+b2) =(3a−5b−3a−5b)[(3a−5b)2+(3a+5b)2+(3a−5b)(3a+5b)]=(−10b)[9a2−2×3a×5b+25b2+9a2+2×3a×5b+25b2+9a2−25b2]=(−10b)[9a2+25b2+9a2+9a2]=(−10b)(27a2+25b2)

Simplify: $(3 a - 5 b)^{3} - (3 a + 5 b)^{3}$