Question
If $a + 2b = 5;$ then show that $: a^3+ 8b^3+ 30ab = 125.$
✓
Answer
Given that $a + 2b = 5$
We need to find $a^3 + 8b^3 + 30ab$
Now consider the cube of $a + 2b$
$( a + 2b )^3 = a^3 + (2b)^3 + 3 \times a \times 2b \times ( a + 2b )$
$( a + 2b )^3 = a^3 + 8b^3 + 6ab \times ( a + 2b )$
$5^3 = a^3 + 8b^3 + 6ab \times 5 [ \because a + 2b = 5 ]$
$125 = a^3 + 8b^3 + 30ab$
Thus the value of $a^3 + 8b^3 + 30ab $ is $125.$
We need to find $a^3 + 8b^3 + 30ab$
Now consider the cube of $a + 2b$
$( a + 2b )^3 = a^3 + (2b)^3 + 3 \times a \times 2b \times ( a + 2b )$
$( a + 2b )^3 = a^3 + 8b^3 + 6ab \times ( a + 2b )$
$5^3 = a^3 + 8b^3 + 6ab \times 5 [ \because a + 2b = 5 ]$
$125 = a^3 + 8b^3 + 30ab$
Thus the value of $a^3 + 8b^3 + 30ab $ is $125.$
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