Question

factorize x(x-2)-y(y-2)​

Answer 1

${x}^{2} - 2x - {y}^{2} + 2y$

Answer 2

Answer:

Try to separate it into different parts and try to use a substitution as follows:

step 1 factorise [math]x^2-y^2[/math] :

[math]x^2-y^2=(x+y)(x-y)[/math]

step 2 let [math]a=x-y[/math] :

so

[math]x^2-y^2+x-y=(x+y)(x-y)+(x-y)[/math]

replacing x-y to [math]a [/math]becomes

[math]x^2-y^2+x-y=(x+y)a+a[/math]

[math] =a((x+y)+1))[/math]

taking back from a the x-y:

[math]a((x+y)+1))=(x-y)(x+y+1)[/math]

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