Question

on factorization of expressions reducible to a³+b³ or a³-b³ form :

1) a³ + 7b³ + 6ab (a+2b)

Answer 1

Answer :





${a }^{3} + 7 {b}^{3} + 6ab(a + 2b)$





Now , splitting 7b^3 into 8b^3-b^3





${a}^{3} + 8 {b}^{3} + 6ab(a + 2b) - {b}^{3}$





Expressing it in the form of identity (a+b)^3=a^3+b^3+3ab(a+b)





${a}^{3} + {(2b)}^{3} + 3 \times 2b \times a(a + 2b) - {b}^{3}$





${(a + 2b)}^{3} - {b}^{3}$





Now using identity a^3-b^3=(a-b)(a^2+b^2+ab)





$(a + 2b - b)( {a}^{2} + 4 {b}^{2} + 4ab + {b}^{2} + ab + 2 {b}^{2} )$





Simplyfying it, we get :-




$(a + b)( {a }^{2} + 5ab + 7 {b}^{2} )$