Question

Expand the following: (i ) (5p - 3q )³ ( ii ) ( 4a - 2b - 3c )². Pls answer it fast don't be late hurry up very urgent

Answer 1

Given : -

[ i ] ( 5p - 3q )³

[ ii ] ( 4a - 2b - 3c )²

Required to find : -

• Expand the given algebraic expressions

Method used : -

Using the algebraic Identities

Identities used : -

( a - b )³ = a³ - b³ - 3a²b + 3ab²

( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

Solution : -

[ i ] ( 5p - 3q )³

[ ii ] ( 4a - 2b - 3c )²

we need to expand these algebraic expressions

So,

Consider the 1st one ;

[ i ]

( 5p - 3q )³

This is in the form of ;

( a - b )³ = a³ - b³ - 3a²b + 3ab²

Using this identity let's expand this algebraic expressions .

Here,

a = 5p

b = 3q

This implies ;

( 5p - 3q )³ =

=> ( 5p )³ - ( 3q )³ - 3 ( 5p )² ( 3q ) + 3 ( 5p ) ( 3q )²

=> 125p³ - 27q³ - 3 ( 25p² ) ( 3q ) + 3 ( 5p ) ( 9q² )

=> 125p³ - 27q³ - 225p²q + 135pq²

[ ii ]

( 4a - 2b - 3c )²

This can also be written as ;

( 4a + [ - 2b ] + [ - 3c ] )²

This is in the form of ;

( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

Using this identity let's expand this algebraic expression .

Here,

a = 4a

b = - 2b

c = - 3c

This implies ;

( 4a - 2b - 3c )² =

=> ( 4a )² + ( - 2b )² + ( - 3c )² + 2 ( 4a ) ( - 2b ) + 2 ( - 2b ) ( - 3c ) + 2 ( - 3c ) ( 4a )

=> 16a² + 4b² + 9c² + ( - 16ab ) + 12bc + ( - 24ca )

=> 16a² + 4b² + 9c² - 16ab + 12bc - 24ca

Therefore,

( 5p - 3q )³ = 125p³ - 27q³ - 225p²q + 135pq²

( 4a - 2b - 3c )² = 16a² + 4b² + 9c² - 16ab + 12bc - 24ca

Additional Information : - >

Some of the algebraic Identities are ;

( a + b ) ( a - b ) = a² - b²

( x + a ) ( x + b ) = x² + x ( a + b ) + ab

( a + b ) ( a + b ) = ( a + b )²

( a - b ) ( a - b ) = ( a - b )²

( x + y )² = x² + 2xy + y²

( x - y )² = x² - 2xy + y²

( x + y )³ = x³ + y³ + 3x²y + 3xy²

All ploynomials can become algebraic expressions .

But,

All algebraic expressions can't become polynomials .