Question

simplify the following
(3x-4y) ^3+(3x+4y) ^3
please give ans with full steps
correct ans ( 54x^3+288xy^2)​

Answer 1

Answer:

simplify: (3x+4y)

3

−(3x−4y)

3

−216x

2

y

We know: (a+b)

3

=a

3

+b

3

+3a

2

b+3ab

2

And (a−b)

3

=a

3

−b

3

−3a

2

b+3ab

2

So,

⇒27x

3

+64y

3

+108x

2

y+144xy

2

−(27x

3

−64y

3

−108x

2

y+144xy

2

)−216x

2

y

⇒128y

3

+216x

2

y−216x

2

y

⇒128y

3

Answer.

Answer 2

Answer:

$(3x-4y)^{3} + (3x+4y)^{3}$

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

[since $a^{3} + b^{3} = (a+b)(a^{2} + b^{2} - ab)$ ]

$= 6x((3x-4y)^{2} + (3x+4y)^{2} - (3x)^{2} + (4y)^{2} )$

[since $(a+b)(a-b)=a^{2} -b^{2}$ ]

$= 6x(9x^{2} -24xy+16y^{2} + 9x^{2} +24xy+16y^{2} - 9x^{2} + 16y^{2} )$

[(a+b)² and (a-b)² identity used]

$=6x(9x^{2} +48y^{2})$

$=54x^{3} + 288xy^{2}$

Hence Verified

PLS MARK AS BRAINLIEST