Question

Factories the expression

8x³+27y³+36x²y+54xy²​

Answer 1

Answer:

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Answer 2

Required answer :–

The given expression can be written as

(2x)³ + (3y)³ + 3(4x²)(3y) + 3(2x)(9y²)

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

= (2x + 3y)³ (Using Identity VI)

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

Now consider (x + y + z)(x² + y² + z² - xy - yz - zx)

On expending, we get the product as

x(x² + y² + z² - xy - yz - zx) + y(x² + y² + z² - xy - yz - zx) + z(x² + y² + z² - xy - yz - zx)

= x³ + xy² + xz² - x²y - xyz - zx² + x²y + y³ + yz² - xy² - y²z - xyz + x²z + y²z + z³ - xyz - yz² - xz²

= x³ + y³ + z³ - 3xyz (On simplification)

So, we obtain the following identity:

x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy - yz - zx)