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प्रश्न
Factorise the following:
a6 – 64
उत्तर
a6 – 64 = a6 – 26
= (a2)3 – (22)3 ...[a3 – b3 = (a – b) + (a2 + ab + b2)]
= (a2 – 22) [(a2)2 + (a2) (22) + (22)2]
= (a + 2) (a – 2) (a4 + 4a2 + 16)
= (a + 2) (a – 2) [(a2)2 + 42 + 8a2 – 4a2]
= (a + 2) (a – 2) [(a2 + 4)2 – (2a)2] ......{a2 – b2 = (a + b) (a – b)}
= (a + 2) (a – 2) (a2 + 4 + 2a) (a2 + 4 – 2a)
= (a + 2) (a – 2) (a2 + 2a + 4) (a2 – 2a + 4)
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संबंधित प्रश्न
Simplify:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
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:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Factorise:
27m3 − 216n3
Factorise:
125y3 − 1
Factorise:
8p3 −\[\frac{27}{p^3}\]
Simplify:
p3 − (p + 1)3
Simplify: (a - b)3 - (a3 - b3)
Factorise the following:
27x3 – 8y3
