find the expression whose square is (2x^2-xy-15y^2) (4x^2-25y^2) (2x^2-11xy+15y^2).
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Answered by
42
To find it's root we will first factorise it :
(2x^2 -xy-15y^2)(4x^2-25y^2)(2x^2 -11xy+ 15y^2)
= ( 2x^2 -6xy + 5xy -15y^2) {(2x)^2 - (5y)^2}
( 2x^2 -6xy -5 xy + 15 y^2)
= {2x ( x - 3y) + 5y (x -3y)}( 2x-5y)(2x+5y)
{ 2x (x -3y) - 5y (x-3y)}
= (2x +5y) (x- 3y)(2x -5y)(2x+5y)(2x -5y)(x-3y)
Now, to we have to find it's square root
=√{(2x +5y) (x- 3y)(2x -5y)(2x+5y)(2x -5y)(x-3y)}
Which equals
(2x +5y) (x- 3y)(2x -5y).
(2x^2 -xy-15y^2)(4x^2-25y^2)(2x^2 -11xy+ 15y^2)
= ( 2x^2 -6xy + 5xy -15y^2) {(2x)^2 - (5y)^2}
( 2x^2 -6xy -5 xy + 15 y^2)
= {2x ( x - 3y) + 5y (x -3y)}( 2x-5y)(2x+5y)
{ 2x (x -3y) - 5y (x-3y)}
= (2x +5y) (x- 3y)(2x -5y)(2x+5y)(2x -5y)(x-3y)
Now, to we have to find it's square root
=√{(2x +5y) (x- 3y)(2x -5y)(2x+5y)(2x -5y)(x-3y)}
Which equals
(2x +5y) (x- 3y)(2x -5y).
Answered by
6
Answer:
To find it's root we will first factorise it :
(2x^2 -xy-15y^2)(4x^2-25y^2)(2x^2 -11xy+ 15y^2)
= ( 2x^2 -6xy + 5xy -15y^2) {(2x)^2 - (5y)^2}
( 2x^2 -6xy -5 xy + 15 y^2)
= {2x ( x - 3y) + 5y (x -3y)}( 2x-5y)(2x+5y)
{ 2x (x -3y) - 5y (x-3y)}
= (2x +5y) (x- 3y)(2x -5y)(2x+5y)(2x -5y)(x-3y)
Now, to we have to find it's square root
=√{(2x +5y) (x- 3y)(2x -5y)(2x+5y)(2x -5y)(x-3y)}
Which equals
(2x +5y) (x- 3y)(2x -5y).
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