Question

solve using identity
${(3a - 5b)}^{3}$


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Answer 1

Answer:

$\large \bold \orange{ \underline{question}} \\ \\ \implies \bold{solve \: \: using \: \: identity \: = (3a - 5b) {}^{3} } \\ \\ \implies \bold \green{formula \: \: \: of \: \: \: (a - b) {}^{3} } \\ \\ \implies \bold \blue {\boxed{(a - b) {}^{3} = {a}^{3} - 3 {a}^{2}b + 3a {b}^{2} - {b}^{3} }} \\ \\ \implies \bold{(3a - 5b) {}^{3} } \\ \\ \implies \bold{(3a) {}^{3} } - 3(3a) {}^{2}5b + 3(3a)(5b) {}^{2} - (5b) {}^{3} \\ \\ \implies \bold{27 {a}^{3} - 135 {a}^{2}b + 225a {b}^{2} - 125 {b}^{3} } \\ \\ \implies \bold \green{ \underline{related \: \: formula}} \\ \\ \implies \bold {1) = (a + b) {}^{3} = a {}^{3} + 3 {a}^{2}b + 3ab {}^{2} + {b}^{3} } \\ \\ \implies \bold{2) = (a - b) {}^{3} = {a}^{3} - 3 {a}^{2}b + 3a {b}^{2} - {b}^{3} } \\ \\ \implies \bold{3) = ( {a}^{3} - {b}^{3}) = (a - b)( {a}^{2} + ab + {b}^{2} ) } \\ \\ \implies \bold{4) = ( {a}^{3} + {b}^{3} ) =(a + b)( {a}^{2} - ab + {b}^{2} ) }$

Answer 2

QUESTION:

solve using identity

$( {3a - 5b})^{3}$

ANSWER:

We use the identity here;

$( {x - y})^{3}$

the expansion of the identity is;

$\huge\organe{{x}^{3} - {y}^{3} - 3xy(x - y)}$

now come to main question;

Here;

3a = x

5b = y

using the identity;

${3a}^{3} - {5b}^{3} - 3 \times 3a \times 5b(3a - 5b) \\ 27 {a}^{3} - 125 {b}^{3} - 45ab(3a - 5b)$

$27 {a}^{3} - 125 {b}^{3} - 135 {a}^{2} b + 225 a{b}^{2}$

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