What is the value of the expression $27 x^{3} + 18 x^{2} y + 12 x y^{2} + y^{3}$ , when $x = 4$ , $y = - 8$ ?

1984

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1782

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1876

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1689

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Solution

The correct option is A 1984
Using the expansion of $(a + b)^{3}$ = $a^{3}$ + $3 a^{2} b + 3 a b^{2} + b^{3}$

$∴$ (3x + y)³ = 27x³ + 3(3x)²y + 3(3x)y² + y³ = 27x³ + 27x²y + 9xy² + y³
So, the given expression is (3x + y)³ – 9x²y + 3xy²
= (3x + y)³ – 3xy ( 3x – y)
= (3 × 4 – 8)³ – {3 $\times$ 4 $\times$ -8 (12 + 8)}
= 4³ + 12 $\times$ 8 $\times$ 20 = 64 + 1920 = 1984

Suggest Corrections

Similar questions

\frac{{(x - y)}^{3} + {(y - z)}^{3} + {(z - x)}^{3}}{(x - y) (y - z) (z - x)}

x^{3} + y^{3} - 12 x y + 64,

x + y = - 4.

x \neq 0

3 x + \frac{1}{3 x} = 8

27 x^{3} + \frac{1}{27 x^{3}}

x \neq 0

3 x + \frac{1}{3 x} = 8

27 x^{3} + \frac{1}{27 x^{3}}

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