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प्रश्न
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
उत्तर
We know that,
a3 + b3 = (a + b)(a2 − ab + b2)
a3 − b3 = (a − b)(a2 + ab + b2)
a2 − b2= (a + b) (a − b)
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
\[ = \frac{\left( m + n \right)\left( m - n \right)}{\left( m + n \right)\left( m + n \right)} \times \frac{\left( m^2 + mn + n^2 \right)}{\left( m - n \right)\left( m^2 + mn + n^2 \right)}\]
\[= \frac{1}{m + n}\]
संबंधित प्रश्न
Simplify:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
Simplify:
\[\frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
Factorise:
y3 − 27
Factorise:
x3 − 64y3
Factorise:
64x3 − 729y3
Simplify:
(x + y)3 − (x − y)3
Simplify:
(a + b)3 − a3 − b3
Factorise: `a^3 - 1/(a^3)`
Simplify: (a - b)3 - (a3 - b3)
Factorise the following:
27x3 – 8y3
