a^6-18a^3+125 *factorisation
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1) 18a^3 is taken as 45a^3 - 27a^3
2) Hence, the given one is = a^6 - 27a^3 + 125 + 45a^3
= (a²)^3 + (-3a)^3 + (5)^3 - 3(a²)(-3a)(5)
3) Now, we can apply, a^3 + b^3 + c^3 - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)
Here a = a²; b = -3a and c = 5
Thus, a^6 + 18a^3 + 125 = (a²)^3 + (-3a)^3 + (5)^3 - 3(a²)(-3a)(5)
= (a² - 3a + 5){(a^4) + 9a² + 25 + 3(a^3) + 15a - 5a²}
= (a² - 3a + 5){(a^4) + 3(a^3) + 4a² + 15a + 25}
2) Hence, the given one is = a^6 - 27a^3 + 125 + 45a^3
= (a²)^3 + (-3a)^3 + (5)^3 - 3(a²)(-3a)(5)
3) Now, we can apply, a^3 + b^3 + c^3 - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)
Here a = a²; b = -3a and c = 5
Thus, a^6 + 18a^3 + 125 = (a²)^3 + (-3a)^3 + (5)^3 - 3(a²)(-3a)(5)
= (a² - 3a + 5){(a^4) + 9a² + 25 + 3(a^3) + 15a - 5a²}
= (a² - 3a + 5){(a^4) + 3(a^3) + 4a² + 15a + 25}
dibakar466:
thanks sir ....u help kn understanding this .....tysm
sir can you solve one more problem plz?
afsarchacha made two wooden chairs with same price and he put the marked price for each chair as rs 1250. he made a prof...
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