Factorise : x^{3}-125 | vedclass

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Question

(A) To factorise the expression $x^{3}-125$,we use the algebraic identity for the difference of two cubes: $a^{3}-b^{3} = (a-b)(a^{2}+ab+b^{2})$.Here,

Vedclass · Accepted Answer

$(x-5)(x^{2}+5x+25)$

Vedclass · Answer

(A) To factorise the expression $x^{3}-125$,we use the algebraic identity for the difference of two cubes: $a^{3}-b^{3} = (a-b)(a^{2}+ab+b^{2})$.Here,$x^{3}-125$ can be written as $x^{3}-5^{3}$.Comparing this with $a^{3}-b^{3}$,we have $a = x$ and $b = 5$.Substituting these values into the identity: $x^{3}-5^{3} = (x-5)(x^{2} + x(5) + 5^{2})$.Simplifying the expression,we get: $(x-5)(x^{2}+5x+25)$.

Factorise $: x^{3}-125$

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