Question

Factorize 2x³ + 5x²y – 12xy²

Answer 1

When we factorize 2x³ + 5x²y – 12xy² we will get  x (2x-3y) (x+4y)

Given:

2x³ + 5x²y – 12xy²

To find:

Factorize 2x³ + 5x²y – 12xy²

Solution:

Given expression 2x³ + 5x²y – 12xy²

Split 5x²y as 8x²y - 3x²y    

⇒ 2x³ + 5x²y – 12xy²  

= 2x³ + 8x²y – 3x²y – 12xy²  

Take common 2x² and – 3xy as shown below

= 2x²(x + 4y) – 3xy (x + 4y)

=  (x + 4y) (2x²-3xy)

Take x common from 2x²-3xy

= (x + 4y) x(2x - 3y)

= x (2x-3y) (x+4y)

Therefore,

When we factorize 2x³ + 5x²y – 12xy² we will get  x (2x-3y) (x+4y)

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Answer 2

Answer:

The answer to the given question is on factorising the given expression we get the simplified value as

$x(2x - 3y)(x + 4y)$

Step-by-step explanation:

Given :

2x³ + 5x²y – 12xy²

To find:

we have to factorise the given expression.

Solution :

The given expression is factorised by the following steps.

Let the given expression by

2x³ + 5x²y – 12xy²

$5 {x}^{2} y \: can \: be \: splited \: as \: 8 {x}^{2} y \: - \: 3 {x}^{2} y$

let's substitute the above value in an expression. we get the values as

$2 {x}^{3} + 8 {x}^{2} y - 3 {x}^{2} y - 12x {y}^{2}$

Taking 2x² as common we get the expression as

$2 {x}^{2} (x + 4y) - 3 {x}^{2} y - 12x {y}^{2}$

again take -3xy as common, we get the value as

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

Then on taking x+4y as common, we get the values as

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

Taking x as a common value the answer will become

$x(2x - 3y)(x + 4y)$

Therefore, on factorising of 2x³ + 5x²y – 12xy²we get the values as

$x(2x - 3y)(x + 4y)$

Hence, the answer is found

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