Question

Find 64x^3 +125y^3 if 4x+5y=19 and xy=5

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

The value of the expression is 1159.

Explanation:

Given expression : $64x^3 +125y^3$

Since $64=4\times4\times4=4^3$ and $125=5\times5\times5=5^3$

So , the above expression will become.

$4^3x^3 +5^3y^3=(4x)^3+(5y)^3$

We know that $(a+b)^3=a^3+b^3+3ab(a+b)$ , then

$a^3+b^3=(a+b)^3-3ab(a+b)$

Similarly

$(4x)^3+(5y)^3=(4x+5y)^3-3(4x)(5y)(4x+5y)$

$=(4x+5y)^3-60xy(4x+5y)$

Substitute the value of 4x+5y=19  and xy=5 (given) , we get

$=(19)^3-60(5)(19)$

$=6859-5700=1159$

Hence, the value of the expression is 1159.

# Learn more :

Fatorise: 27x^3 - 125y^3​

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