Question

16(2x-1)^2-25y^2 factorize ​

Answer 1

Answer:

( 8x + 5y - 4 ) ( 8x - 5y - 4 )

Step-by-step explanation:

Given------> 16 ( 2x - 1 )² - 25 y²

To find-----> Factors of given expression

Solution------> We know that,

a² - b² = ( a + b ) ( a - b )

We know that

16 = 2 × 2 × 2 × 2

= 4 × 4

16 = 4²

25 = 5 × 5

= 5²

Now returning to original problem,

16 ( 2x - 1 )² - 25 y²

= ( 4 )² ( 2x - 1 )² - ( 5 )² y²

We know that , aᵐ bᵐ = ( ab )ᵐ applying it we get,

= { 4 ( 2x - 1 ) }² - ( 5 y )²

= ( 8x - 4 )² - ( 5y )²

Applying above identity , we get,

= { ( 8x - 4 ) + 5y } { ( 8x - 4 ) - 5y }

= ( 8x - 4 + 5y ) ( 8x - 4 - 5y )

= ( 8x + 5y - 4 ) ( 8x - 5y - 4 )

Additional information----->

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

3) ( a + b )³ = a³ + b³ + 3ab ( a + b )

4) ( a - b )³ = a³ - b³ - 3ab ( a - b )

5) ( a³ + b³ ) = ( a + b ) ( a² + b² - ab )

6) ( a³ - b³ ) = ( a - b ) ( a² + b² + ab )

Answer 2

Step-by-step explanation:

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