Question

factorise (1-x)³ + (y-1)³ +(x-y)³
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Answer 1

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Answer 2

$\huge{\underline{\underline{\red{♡Solution→}}}}$

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$( {1 - x)}^{3} + ( {y - 1)}^{3} + ( {x - y)}^{3}$

We know the formula →

$( {a - b)}^{3} = {a}^{3} - {b}^{3} - 3ab(a - b)$

According to this formula →

$= 1 - {x}^{3} - 3 \times x(1 - x) + {y}^{ 3} - 1 - 3 \times y(y - 1) + {x}^{3} - {y}^{3} - 3 \times x \times y(x - y) \\ = - {x}^{3} - 3x(1 - x) + {y}^{3} - 3y(y - 1) + {x}^{3} - {y}^{3} - 3xy(x - y) \\ = - 3x(1 - x) - 3y(y - 1) - 3xy( x- y)</strong><strong>\</strong><strong>\</strong><strong> </strong><strong>=</strong><strong> </strong><strong>3</strong><strong>(</strong><strong>1</strong><strong>-</strong><strong>x</strong><strong>)</strong><strong>(</strong><strong>y-1</strong><strong>)</strong><strong>(</strong><strong>x-y</strong><strong>)</strong><strong>$

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