Question

if (3x-4)3 = 27x3 - 64y3 +ax2y +bxy2 then find the value of a+b.

Answer 1

Hi

( 3x-4y)³ = 27x³ - 64y³ +ax²y+bxy² --(1)

Expand ( 3x - 4y )³

= ( 3x )³- (4y)³+3(3x)² (-4y) + 3(3x)(-4y)²

= 27x³-64y³ + (-108)x²y + (144)xy--(2)

Compare ( 1 ) and ( 2 ) ,

a = - 108 ,

b = 144

I hope this helps you.

: )

Answer 2

Answer to the question :

So need a formula, (a-b)³=a³-3a²b+3ab²-b³
(3x-4y)³=(3x)³-3.(3x)².4y+3.3x.(4y)²-(4y)³
or, (3x-4)³= 27x³-108x²y+144xy²-64y³
or, (3x-4)³=27x³+(-108)x²y+144xy²-64y³
or, (3x-4)³=27x³-64y³+(-108)x²y+144xy²

Now if you compare (3x-4)³= 27x³-64y³+ax²y+bxy² with (3x-4)³=27x³-64y³+(-108)x²y+144xy² then you will find a= -108 and b= 144