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प्रश्न
Simplify:
(3a + 5b)3 − (3a − 5b)3
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उत्तर
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
संबंधित प्रश्न
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Simplify:
\[\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Factorise:
8p3 −\[\frac{27}{p^3}\]
Factorise:
343a3 − 512b3
Simplify:
p3 − (p + 1)3
Simplify: (a - b)3 - (a3 - b3)
Simplify: (2x + 3y)3 - (2x - 3y)3
Factorise the following:
27x3 – 8y3
