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प्रश्न
Simplify:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
उत्तर
It is known that,
a2 − b2 = (a + b) (a − b)
a3 − b3 = (a − b)(a2 + ab + b2)
\[\ \frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
\[ = \frac{\left( 2x \right)^3 - \left( 3y \right)^3}{\left( 2x \right)^2 - \left( 3y \right)^2}\]
\[ = \frac{\left( 2x - 3y \right)\left[ \left( 2x \right)^2 + \left( 2x \right) \times \left( 3y \right) + \left( 3y \right)^2 \right]}{\left( 2x + 3y \right)\left( 2x - 3y \right)}\]
\[= \frac{\left(2x - 3y \right)\left(4 x^2 + 6xy + 9 y^2 \right)}{\left( 2x + 3y \right)\left(2x - 3y \right)}\]
\[= \frac{4 x^2 + 6xy + 9 y^2}{\left(2x + 3y \right)}\]
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:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Factorise:
y3 − 27
Factorise:
x3 − 64y3
Factorise:
125y3 − 1
Simplify:
p3 − (p + 1)3
Factorise: x3 - 8y3
Factorise: 27p3 - 125q3.
Factorise the following:
a6 – 64
