Simplify (2 x-5 y)^{3}-(2 x+5 y)^{3} | vedclass

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Question

(A) We use the algebraic identity $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$.Let $a = (2x - 5y)$ and $b = (2x + 5y)$.Then,$a - b = (2x - 5y) - (2x + 5y) = 2x

Vedclass · Accepted Answer

$-120 x^{2} y-250 y^{3}$

Vedclass · Answer

(A) We use the algebraic identity $a^{3}-b^{3}=(a-b)(a^{2}+ab+b^{2})$.Let $a = (2x - 5y)$ and $b = (2x + 5y)$.Then,$a - b = (2x - 5y) - (2x + 5y) = 2x - 5y - 2x - 5y = -10y$.Now,calculate $a^{2} + ab + b^{2}$:$a^{2} = (2x - 5y)^{2} = 4x^{2} + 25y^{2} - 20xy$$b^{2} = (2x + 5y)^{2} = 4x^{2} + 25y^{2} + 20xy$$ab = (2x - 5y)(2x + 5y) = 4x^{2} - 25y^{2}$Summing these: $(4x^{2} + 25y^{2} - 20xy) + (4x^{2} - 25y^{2}) + (4x^{2} + 25y^{2} + 20xy) = 12x^{2} + 25y^{2}$.Finally,multiply $(a - b)$ and $(a^{2} + ab + b^{2})$:$(-10y)(12x^{2} + 25y^{2}) = -120x^{2}y - 250y^{3}$.

Simplify $(2 x-5 y)^{3}-(2 x+5 y)^{3}$

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