What is the standard form of f=(x−2)(x−y)2?

Question

bekiffen32 · Accepted Answer

Explanation:
To rewrite a function in standard form, expand the brackets:

f (x) = (x - 2) {(x - y)}^{2}

f(x)=(x-2)(x-y)(x-y)

f (x) = (x - 2) (x^{2} - x y - x y + y^{2})

f (x) = (x - 2) (x^{2} - 2 x y + y^{2})

f (x) = (x^{3} - 2 x^{2} y + x y^{2} - 2 x^{2} + 4 x y - 2 y^{2})

f (x) = (x^{3} - 2 x^{2} y + x y^{2} - 2 x^{2} - 2 y^{2} + 4 x y)

nebajcioz · Accepted Answer

Explanation:  Given:(x−2)(x−y)2...(1)  Consider (x−y)2  Write as (x-y)(x-y)  This is distributive so we have:  Every part of the blue bracket is multiplied by all of the brown bracket:  x(x-y)-y(x-y)  Giving:  x2−xy−xy+y2  x2−2xy+y2...(2)  Substitute (2) into (1) for (x−y)2 giving:  (x−2)(x2−2xy+y2)  Every part of the blue bracket is multiplied by all of the brown bracket:  x(x2−2xy+y2)−2(x2−2xy−2y2)  Giving:  x3−2x2y+xy2−2x2+4xy−2y2  Changing the order giving x precedence over y  x3−2x2−2x2y+4xy+xy2−2y2

What is the standard form of f=(x-2)(x-y)^{2}?

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