Question

$\bf{Answer \: this \:correctly \: and \: do \: not \: spam}$
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Answer 1

Answer:

-224

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Prerequisite knowledge:

• (a - b)³ = a³ - b³ - 3ab(a - b)

• Negative × Negative = Positive

• Positive × Negative = Negative

• The cube of any negative natural number will be negative.

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Step-by-step explanation:

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We've been given that;

• (a - b) = -8

• ab = 12

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And we're asked to find the value of a³ - b³.

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ATQ;

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$\sf \dashrightarrow (a - b) = -8$

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We're asked to find the value of a³ and b³, so we'll need both these terms in the equation. We can cube both sides of the equation to achieve that.

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$\sf \dashrightarrow (a - b)^{\bf{3}} = (-8)^{\bf{3}}$

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On applying the identity (a - b)³ = a³ - b³ - 3ab(a - b) we get;

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$\sf \dashrightarrow (a)^3 - (b)^3 - 3ab(a - b) = (-8)^3$

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$\sf \dashrightarrow a^3 - b^3 - 3ab(a - b) = 512$

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We know that;

• a - b = -8

• ab = 12

On substituing both these values we get;

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$\sf \dashrightarrow a^3 - b^3 - 3(12)(-8) = 512$

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$\sf \dashrightarrow a^3 - b^3 - 3(-96) = 512$

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$\sf \dashrightarrow a^3 - b^3 + 288 = 512$

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On transposing 288 to the RHS we get;

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$\sf \dashrightarrow a^3 - b^3 = 512 - 288$

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$\sf \dashrightarrow \textsf{\textbf{a}}^3 - \textsf{\textbf{b}}^3 = \textsf{\textbf{-224}}$

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Therefore, the answer is Option(1): -224

Answer 2

$\bf \color{navy}Answer:$

$\huge\tt \color{red}-244$

$\bf \color{navy}Step-by-step \: explanation:$

$\bf(a - b) \: = - 8, \: ab = 12$

$\bf {a}^{3} - {b}^{3} = {(a - b)}^{3} + 3ab \: (a-b)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf= (-8)^{3} + 3 (-12) (-8)$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf= -512 + 288$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf= -224$