Simplify the following :

$(i) {(5 a - 8 b)}^{2} - {(5 a + 8 b)}^{2}$

$(i i) {(2 a + 3 b)}^{2} - ((2 a + 3 b) (2 a - 3 b))$ [4 MARKS]

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Solution

Application: 2 Marks each

$(i) {(5 a - 8 b)}^{2} - {(5 a + 8 b)}^{2}$

$= ((5 a - 8 b) + (5 a + 8 b)) ((5 a - 8 b) - (5 a + 8 b))$

$= (5 a - 8 b + 5 a + 8 b) (5 a - 8 b - 5 a - 8 b)$

$= (10 a) (- 16 b)$

$= - 160 a b$

$(i i) {(2 a + 3 b)}^{2} - (2 a + 3 b) (2 a - 3 b)$

$= {(2 a + 3 b)}^{2} - [{(2 a)}^{2} - {(3 b)}^{2}]$

$= {(2 a + 3 b)}^{2} - 4 a^{2} + 9 b^{2}$

$= (2 a)^{2} + (3 b)^{2} + 2 (2 a) (3 b) - 4 a^{2} + 9 b^{2}$

$= 4 a^{2} + 9 b^{2} + 12 a b - 4 a^{2} + 9 b^{2}$

$= 18 b^{2} + 12 a b$

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Similar questions

Simplify the following :

$(i) {(5 a - 8 b)}^{2} - {(5 a + 8 b)}^{2}$

$(i i) {(2 a + 3 b)}^{2} - ((2 a + 3 b) (2 a - 3 b))$ [4 MARKS]

What is the LCM of $(2 a + 3 b)^{2}$ and $(4 a^{2} - 9 b^{2})$

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