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Step-by-step explanation:
: 64x^3 +125y^364x
3
+125y
3
Since 64=4\times4\times4=4^364=4×4×4=4
3
and 125=5\times5\times5=5^3125=5×5×5=5
3
So , the above expression will become.
4^3x^3 +5^3y^3=(4x)^3+(5y)^34
3
x
3
+5
3
y
3
=(4x)
3
+(5y)
3
We know that (a+b)^3=a^3+b^3+3ab(a+b)(a+b)
3
=a
3
+b
3
+3ab(a+b) , then
a^3+b^3=(a+b)^3-3ab(a+b)a
3
+b
3
=(a+b)
3
−3ab(a+b)
Similarly
(4x)^3+(5y)^3=(4x+5y)^3-3(4x)(5y)(4x+5y)(4x)
3
+(5y)
3
=(4x+5y)
3
−3(4x)(5y)(4x+5y)
=(4x+5y)^3-60xy(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)=(19)
3
−60(5)(19)
=6859-5700=1159=6859−5700=1159
Hence, the value of the expression is 1159.
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