Question

If 2a+3b=7and ab=2, find8a³+27b³​

Answer 1

Answer:

$28 {a}^{2} - 84 + 9 {b}^{2}$

Step-by-step explanation:

$8 {a}^{3} + 27 {b}^{3} \\ =( {2a})^{3} + ( {3b})^{3}$

According to the formula,

${x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} ) \\ = > (2a + 3b)(( {2a})^{2} - 2a \times 3b + ( {3b})^{2} ) \\ = > (2a + 3b)(4 {a}^{2} - 6ab + 9 {b}^{2} )$

By given data,

$7(4 {a}^{2} - 6(2) + 9 {b}^{2} ) \\ = > 7(4 {a}^{2} - 12 + 9 {b}^{2} ) \\ = > 28 {a}^{2} - 84 + 9 {b}^{2}$

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Answer 2

Answer:

595

Step-by-step explanation:

We know that,

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

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

Here, a = 2a ; b = 3b

{ 8a^3 + 27b^3 = (2a)^3 + (3a)^3}

On substituting,

$(2a) {}^{3} + (3b) {}^{3} \\ = (2a + 3b) {}^{3} + 3 \times 2a \times 3b(2a + 3b) \\ = (2a + 3b) {}^{3} + 18ab(2a + 3b) \\ = (2a + 3b)(2a + 3b) {}^{2} + 18ab$

2a+3b = 7

ab =2

On substituting,

$= 7 {}^{3} + 18 \times 2 \times 7 \\ = 343 + 252 \\ = 595$

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