Question

Solve with step by step explaination to be the Brainliest ​

Answer 1

Answer:

-19x^3+35y^3+105x^2+y-57xy^2

Step-by-step explanation:

8(x^3+y^3+3x^2y+3xy^2)-27(x^3-y^3+-3x^2y+3xy^2)

=(8x^3+8y^3+24x^2y+24xy^2)-(27x^3-27y^3-81x^2y+81xy^2)

=8x^3+8y^3+24x^2y+24xy^2-27x^3+27y^3+81x^2y-81xy^2

=-19x^3+35y^3+105x^2+y-57xy^2

Answer 2

Question:

Factorise: 8(x+y)³ - 27(x-y)³

Answer:

- [ x - 5y ]•[ 19x² - 10xy + 7y² ]

Note:

• (A+B)² = A² + 2•A•B + B²

• (A-B)² = A² - 2•A•B + B²

• A² - B² = (A+B)•(A-B)

• (A+B)² = (A-B)² + 4•A•B

• (A-B)² = (A+B)² - 4•A•B

• (A+B)³ = A³ + 3•A•B•(A+B) + B³

• (A-B)³ = A³ - 3•A•B•(A-B) + B³

• A³ + B³ = (A+B)•(A² - A•B + B³)

• A³ + B³ = (A-B)•(A² + A•B + B³)

• (A+B+C)² = A² + B² + C² + 2•(A•B + B•C + C•A)

Solution:

We have;

=> 8(x+y)³ - 27(x-y)³

=> 2³(x+y)³ - 3³(x-y)³

=> [ 2(x+y) ]³ - [ 3(x-y) ]³

=> [ 2(x+y) - 3(x-y) ]•[ {2(x+y)}² + 2(x+y)•3(x-y)

+ {3(x-y)}² ]

=> [ 2(x+y) - 3(x-y) ]•[ 4(x² + y² + 2xy) + 6(x² - y²)

+ 9(x² + y² - 2xy) ]

=> [ 2x + 2y - 3x + 3y ]•[ 4x² + 4y² + 8xy + 6x² - 6y²

+ 9x² + 9y² - 18xy ]

=> [ - x + 5y ]•[ 19x² - 10xy + 7y² ]

=> - [ x - 5y ]•[ 19x² - 10xy + 7y² ]

Hence,

The required answer is ;

- [ x - 5y ]•[ 19x² - 10xy + 7y² ]