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Polynomials

2 x-3 y3+4 z-...

Question

(2x − 3y)³ + (4z − 2x)³ + (3y − 4z)³

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Solution

The given expression to be factorized is

Let, and. Then the given expression becomes

Note that

Recall the formula

When, this becomes

So, we have the new formula

, when.

Using the above formula, the given expression can be written as

Put, and. Then we have

We cannot further factorize the expression.

So, the required factorization is ofis .

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Similar questions

Q. Factorise the following:

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

Q. Find the value of

{(\frac{1}{2} x - \frac{1}{3} y)}^{3} + {(\frac{1}{3} y - \frac{1}{4} z)}^{3} + {(\frac{1}{4} z - \frac{1}{2} x)}^{3} = m (\frac{1}{2} x - \frac{1}{3} y) (\frac{1}{3} y - \frac{1}{4} z) (\frac{1}{4} z - \frac{1}{2} x)

m

Q. The factors of

(2 x - 3 y)^{3} + (3 y - 4 z)^{3} + 8 (2 z - x)^{3}

{(2 x - 3 y)}^{3} + {(3 y - 5 z)}^{3} + {(5 z - 2 x)}^{3}

2 x + 3 y + z = 15

, then value of

(5 - 2 x)^{3} + (5 - 3 y)^{3} + (5 - z)^{3} - 3 (5 - 2 x) (5 - 3 y) (5 - z)

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