We are given that, (9a 5b)^2+186ab = (9a+5b)^2 So, ∴ (9a 5b)^2 (9a+5b)^2 = 186ab now, a^2 b^2 = (a+b)(a b) ∴ (9a 5b+9a+5b)(9a 5b 9a 5b) = 18 ...

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Cube Numbers

9a-5b2+186ab=...

Question

Show that: $(9 a - 5 b)^{2} + 180 a b = (9 a + 5 b)^{2}$ .

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Solution

LHS: $(9 a - 5 b)^{2} + 180 a b$
$= (9 a)^{2} + (5 b)^{2} - 2 \times 9 a \times 5 b + 180 a b$
$= (9 a)^{2} + (5 b)^{2} - 90 a b + 180 a b$
$= (9 a)^{2} + (5 b)^{2} + 90 a b$
$= (9 a)^{2} + (5 b)^{2} + 2 \times 9 a \times 5 b$
$= (9 a + 5 b)^{2}$ .
$=$ RHS
Hence, proved.

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