Question

25(3x-4y)^2-40(9x^2-16y^2)+16(3x+4y)^2​

Answer 1

Answer:

( 3x - 36y )^2

Step-by-step-explanation:

Let,

( 3x - 4y ) = a

( 3x + 4y ) = b

Given equation is : 25( 3x - 4y )^2 - 40( 9x^2 - 16y^2 ) + 16( 3x + 4y )^2.

Now, if you observe the equation, there is a term 9x^2 - 16y^2 which can also be written as ( 3x )^2 - ( 4y )^2 , and now this equation is in the form if a^2 - b^2{ these variables, in this statement, are different from the variables taken in solution } where a represents 3x and b represents 4y. And, from the properties of factorisation we know a^2 - b^2 = ( a + b )( a - b ).

Therefore,

= > 25( 3x - 4y )^2 - 40( 9x^2 - 16y^2 ) + 16( 3x + 4y )^2

= > 25( 3x - 4y )^2 - 40( 3x - 4y )( 3x + 4y ) + 16( 3x + 4y )^2

Replacing ( 3x - 4y ) by a and ( 3x + 4y ) by b :

= > 25a^2 - 40ab + 16b^2.

= > ( 5a )^2 - 2( 5a x 4b ) + ( 4b )^2

= > ( 5a - 4b )^2 { from the properties of factorisation, a^2 - 2ab + b^2 = ( a - b )^2 }

Substituting the correct value of a and b :

= > { 5( 3x - 4y ) - 4( 3x + 4y ) }^2

= > { 15x - 20y - 12x - 16y }^2

= > ( 3x - 36y )^2

Hence the required factorisation of 25( 3x - 4y )^2 - 40( 9x^2 - 16y^2 ) + 16( 3x + 4y )^2 is ( 3x - 36y )^2.

Answer 2

plz MARK AS BRAINLIEST❤