Question

simplify (x-2y)(y-3x)+(x+y)(x-3y)-(y-3x)(4x-5y)

Answer 1

Answer: Simplifying the given equation, we get 10x^2 +14xy.

Step-by-step explanation:

Given that

(x-2y)(y-3x)+(x+y)(x-3y)-(y-3x)(4x-5y)

Applying the distributive property, we see that

x(y-3x) - 2y(y-3x) + x(x-3y) + y(x-3y) - (y(4x-5y) - 3x(4x-5y))

Applying the distributive property again, we get:

x*y - x*3x - 2y*y + 2y*3x + x*x - x*3y + y*x - y*3y - (y*4x - y*5y - 3x*4x + 3x*5y)

=> xy - 3x^2 - 2y^2 + 6xy + x^2 - 3xy + xy-3y^2 - 4xy + 5y^2 + 12x^2 - 15xy

Combining the expression with same bases, we see that

=> (- 3x^2+x^2+12x^2) + (- 2y^2-3y^2+ 5y^2) + (xy + 6xy-3xy+xy-4xy-15xy)

=> 10x^2 + 0y^2 + 14xy

=> 10x^2 +14xy