Question

Find the value of 27 x cube + 8y cube if 3x + 2y =14 and xy=8 .

Answer 1

Here we go!
$27 {x}^{3} + 8 {y}^{3} \\ = {(3x)}^{3} + {(2y)}^{3} \\ = {(3x + 2y)}^{3} - 3 \times 3x \times 2y \times (3x + 2y) \\ = {(14)}^{3} - 18xy \times 14 \\ = 2744 - 18 \times 8 \times 14 \\ = 2744 - 2016 \\ = 728$
I hope you find this useful

[formulas used here-
{a}^{3}+{b}^{3}= {a+b} ^{3} - 3.3x.2y.(3x+2y)]
[ in step 3: given that 3x+2y=14 and xy=8]

Answer 2

Heya user 
Here is your answer !!

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27x³ + 8y³
= ( 3x )³ + ( 2y )³
= ( 3x + 2y )³ - 3 * 3x * 2y ( 3x + 2y )
= ( 3x + 2y )³ -18xy ( 3x + 2y )
= ( 14 )³ - ( 8 * 18 * 14 ) [ putting the values of ( 3x + 2y ) and xy ]
= 2744 - 2016
= 728 . { ANSWER }

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Hope it helps !!