Question

What do we get after factorizing x^{3}+ 8y^{3}+ z^{3} – 4xyz?

- (x + 2y + z) (x
^{2} + 4y^{2} + z^{2} – 2xy – 2yz – zx) - (x + 2y + z) (x
^{2} + 4y^{2} + z^{2} – 2xy – 2yz – zx) - (x + 2y + z) (x
^{2} + 4y^{2} + z^{2} – 2xy – 2yz – zx) - (x + 2y + z) (x
^{2} + 4y^{2}+ z^{2} – 2xy – 2yz – zx)

^{2}+ 4y^{2}+ z^{2}– 2xy – 2yz – zx)^{2}+ 4y^{2}+ z^{2}– 2xy – 2yz – zx)^{2}+ 4y^{2}+ z^{2}– 2xy – 2yz – zx)^{2}+ 4y^{2}+ z^{2}– 2xy – 2yz – zx)## The correct answer is: (x + 2y + z) (x^{2} + 4y^{2} + z^{2} – 2xy – 2yz – zx)

STEP BY STEP SOLUTION

We know that a^{3} + b^{3} + c^{3} – 3abc = (a + b - c) (a^{2} + b^{2} + c^{2} – ab – bc – ca)

In x^{3} + 8y^{3} + y^{3} – 6xyz, a = x, b = 2y and c = z

By using the above equation, we get x^{3} + 8y^{3} + z^{3} – 4xyz = (x+2y+z) (x^{2} + (2y)^{2} + z^{2} – x(2y) – (2y)(z) – zx)

= (x + 2y + z) (x^{2} + 4y^{2} + z^{2} – 2xy – 2yz – zx).

^{3}+ b

^{3}+ c

^{3}– 3abc = (a + b - c) (a

^{2}+ b

^{2}+ c

^{2}– ab – bc – ca)

In x

^{3}+ 8y

^{3}+ y

^{3}– 6xyz, a = x, b = 2y and c = z

^{3}+ 8y

^{3}+ z

^{3}– 4xyz = (x+2y+z) (x

^{2}+ (2y)

^{2}+ z

^{2}– x(2y) – (2y)(z) – zx)

^{2}+ 4y

^{2}+ z

^{2}– 2xy – 2yz – zx).

### Related Questions to study

### Which term will be the middle term of (xyz – x)^{2n}?

### Which term will be the middle term of (xyz – x)^{2n}?

### What do we get after factorizing x^{2 }+ 6x - 27?

### What do we get after factorizing x^{2 }+ 6x - 27?

### Find the value of *k* if x - 3 is a factor of 5x^{3 }- 2x^{2 }+ x + k.

### Find the value of *k* if x - 3 is a factor of 5x^{3 }- 2x^{2 }+ x + k.

### What is the value of *n*, if the coefficients of the second term of (x – y)^{3} is equal to the third term of the expansion (x + y)^{n}?

### What is the value of *n*, if the coefficients of the second term of (x – y)^{3} is equal to the third term of the expansion (x + y)^{n}?

Find the 7^{th} term.

Find the 7^{th} term.

### The degree of the polynomial 8 is ___________.

### The degree of the polynomial 8 is ___________.

Expand.

Expand.

### Find the 4^{th} term of the binomial expansion of .

### Find the 4^{th} term of the binomial expansion of .

### The polynomial which has only one term is called ___________.

### The polynomial which has only one term is called ___________.

Find the 4^{th} term.

Find the 4^{th} term.

The polynomial which has two terms is called ___________.

The polynomial which has two terms is called ___________.

Expand.

Expand.

### Find the 12^{th} term.

### Find the 12^{th} term.

What is the expansion of (x + y)^{1000}?

What is the expansion of (x + y)^{1000}?