Question

Factorise:45x⁴y+6x³y²-72y³x²

plz give proper ans other wise I'll report u
and plz give step by step explanation​

Answer 1

Step-by-step explanation:

Solution:-

Step1)Take 3x²y as common

(3x²y)(15x²+2xy-24y²)

Step2) Now factorize the second term=(15x²+2xy-24y²)

Step3)To factorize this term, simply explit the middle part '2xy' into '20xy-18xy'

Step4)(3x²y)(15x²+2xy-24y²)=(3x²y)(15x²+20xy-18xy-24y²)

=(3x²y){5x(3x+4y)-6y(3x+4y)}

taking out 3x+4y as common we get

=(3x²y){(3x+4y)(5x-6y)}

=(3x²y)(3x+4y)(5x-6y)

hence,45x⁴y+6x³y²-72y³x²=(3x²y)(3x+4y)(5x-6y)

Second method:-

Simply explit the second term of the given equation

45x⁴y+6x³y²-72y³x³y=45x⁴y+60x³y²

-54x³y²-72y³x²

=15x³y(3x+4y)-18x²y²(3x+4y)

=(15x³y-18x²y²)(3x+4y)

=(3x²y)(3x+4y)(5x-6y)

Answer 2

Given : 45x⁴y+6x³y²-72y³x²

To Find : Factorize.

Solution:

45x⁴y+6x³y²-72y³x²

Use middle term split

= 45x⁴y+60x³y²-54x³y²-72y³x²

tale common  15x³y in 1st two terms  and   - 18x²y² in last two terms

= 15x³y(3x + 4y) - 18x²y²(3x + 4y)

Take (3x + 4y) common

= (3x + 4y)( 15x³y -  18x²y²)

Take 3x²y

=  (3x + 4y)3x²y(5x -  6y)

rearrange terms

=  3x²y  (3x + 4y)(5x -  6y)

45x⁴y+6x³y²-72y³x²  =  3x²y  (3x + 4y)(5x -  6y)

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