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Question
Simplify:
(3a + 5b)3 − (3a − 5b)3
Simplify
Solution
It is known that,
a3 − b3 = (a − b)(a2 + ab + b2)
(3a + 5b)3 − (3a − 5b)3
= {(3a + 5b) − (3a − 5b)}{(3a + 5b)2 + (3a + 5b)(3a − 5b) + (3a − 5b)2}
= 10b(9a2 + 25b2 + 30ab + 9a2 + 25b2 − 30ab + 9a2 − 25b2)
= 10b (27a2 + 25b2)
= 10b × 27a2 + 10b × 25b2
= 270a2b + 250b3
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RELATED QUESTIONS
Simplify:
\[\frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
Factorise:
x3 − 64y3
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27m3 − 216n3
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343a3 − 512b3
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64x3 − 729y3
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`16a^3 - 128/b^3`
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p3 − (p + 1)3
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Factorise: 27p3 - 125q3.
Factorise: 54p3 - 250q3.
