Factorise the following: 64 a^{3}-27 b^{3}-14 | vedclass

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Question

(A) The given expression is $64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2}$.This can be rewritten as $(4 a)^{3}-(3 b)^{3}-3(4 a)^{2}(3 b)+3(4 a)(3 b)^{2}$

Vedclass · Accepted Answer

$(4a - 3b)^3$

Vedclass · Answer

(A) The given expression is $64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2}$.This can be rewritten as $(4 a)^{3}-(3 b)^{3}-3(4 a)^{2}(3 b)+3(4 a)(3 b)^{2}$.This expression follows the algebraic identity $(x-y)^{3} = x^{3}-y^{3}-3x^{2}y+3xy^{2}$,where $x = 4a$ and $y = 3b$.Therefore,the expression simplifies to $(4 a-3 b)^{3}$.Thus,the factors are $(4 a-3 b)(4 a-3 b)(4 a-3 b)$.

Factorise the following: $64 a^{3}-27 b^{3}-144 a^{2} b+108 a b^{2}$

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