Question : What is the value of $\left(27 x^3-58 x^2 y+31 x y^2-8 y^3\right)$, when $x=-5$ and $y=-7?$
Option 1: 1924
Option 2: – 1924
Option 3: – 1926
Option 4: 1926
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Correct Answer: 1924
Solution : Given: $x=-5$ and $y=-7$ $\left(27 x^3-58 x^2 y+31 x y^2-8 y^3\right)$ $= (3x)^3-3×(3x)^2×2y+3×3x×(2y)^2-(2y)^3-4x^2y-5xy^2$ $= (3x-2y)^3-xy(4x+5y)$ $= (3×(-5)-2×(-7))^3-(-5×(-7))(4×(-5)+5×(-7))$ $=-1-35(-20-35)$ $= -1-35(-55)$ $= -1+1925$ $= 1924$ Hence, the correct answer is 1924.
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