Question

Using the product of algebraic expressions ,find the formulae for (a+b)3


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Answer 1

DERIVATION OF A PLUS B WHOLE CUBE FORMULA:

Do you know how we got the

${ \left( a+b \right) }^{ 3 } (a+b) </p><p>3$

value?

Yes, now we will see the derivation of the formula.

We know that

${ \left( a+b \right) }^{ 3 } (a+b) </p><p>3$

$= (a + b) x { \left( a+b \right) }^{ 2 } (a+b) </p><p>2$

=

$a+b) x ( { a }^{ 2 } a </p><p>2</p><p> +2ab+ { b }^{ 2 } b </p><p>2</p><p> ) </p><p>$

=

$a ( { a }^{ 2 } a </p><p>2</p><p> + 2 a b + { b }^{ 2 } b </p><p>2$

)l

$+ b ( { a }^{ 2 } a </p><p>2</p><p> + 2 a b + { b }^{ 2 } b </p><p>2</p><p> )</p><p></p><p> = { a }^{ 3 } a </p><p>3$

$+ 2 { a }^{ 2 } a </p><p>2</p><p> b + a { b }^{ 2 } b </p><p>2</p><p> + { a }^{ 2 } a </p><p>2</p><p> b + 2 a { b }^{ 2 } b </p><p>2</p><p> + { b }^{ 3 } b </p><p>3$

$= { a }^{ 3 } a </p><p>3</p><p> + { b }^{ 3 } b </p><p>3</p><p> + 3 { a }^{ 2 } a </p><p>2</p><p> b + 3 a { b }^{ 2 } b </p><p>2</p><p> </p><p></p><p> = { a }^{ 3 } a </p><p>3</p><p> + { b }^{ 3 } b </p><p>3</p><p> + 3 a b (a + b)</p><p>$

HOPE ITS HELP U

Answer 2

Answer:

DERIVATION OF A PLUS B WHOLE CUBE FORMULA:

Do you know how we got the

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

value?

Yes, now we will see the derivation of the formula.

We know that

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

$= (a + b) x { ( a+b ) }^{ 2 } (a+b) 2</p><p> </p><p></p><p>$

$(a+b) x ( { a }^{ 2 } a 2 +2ab+ { b }^{ 2 } b 2 )a+b)x</p><p></p><p>$

=

$a ( { a }^{ 2 } a 2 + 2 a b + { b }^{ 2 } b 2a)$

)l

$</p><p>+ b ( { a }^{ 2 } a 2 + 2 a b + { b }^{ 2 } b 2 ) = { a }^{ 3 } a 3$

$</p><p>+ 2 { a }^{ 2 } a 2 b + a { b }^{ 2 } b 2 + { a }^{ 2 } a 2 b + 2 a { b }^{ 2 } b 2 + { b }^{ 3 } b 3</p><p>$

$</p><p>= { a }^{ 3 } a 3 + { b }^{ 3 } b 3 + 3 { a }^{ 2 } a 2 b + 3 a { b }^{ 2 } b 2 = { a }^{ 3 } a 3 + { b }^{ 3 } b 3 + 3 a b (a + b)$

Hope it helps u