Factorise the following: 27-125 a^{3}-135 a+2 | vedclass

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Question

(A) The given expression is $27-125 a^{3}-135 a+225 a^{2}$.We can rewrite this as $(3)^{3}-(5 a)^{3}-3(3)^{2}(5 a)+3(3)(5 a)^{2}$.This expression foll

Vedclass · Accepted Answer

$(3-5a)^3$

Vedclass · Answer

(A) The given expression is $27-125 a^{3}-135 a+225 a^{2}$.We can rewrite this as $(3)^{3}-(5 a)^{3}-3(3)^{2}(5 a)+3(3)(5 a)^{2}$.This expression follows the algebraic identity $(x-y)^{3} = x^{3}-y^{3}-3x^{2}y+3xy^{2}$.Here,$x = 3$ and $y = 5a$.Therefore,$27-125 a^{3}-135 a+225 a^{2} = (3-5a)^{3}$.This can be written as $(3-5a)(3-5a)(3-5a)$.

Factorise the following: $27-125 a^{3}-135 a+225 a^{2}$

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