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Expand binomial using binomial expansion (x-y)^3

Sagot :

The expression is,

[tex](x-y)^3[/tex]

Expanding the expression we get,

[tex](x-y)^3=(x-y)(x-y)^2\ldots.(1)[/tex]

We have,

[tex](x-y)^2=x^2-2xy+y^2\ldots..(2)[/tex]

Substituting equation 2 in equation 1, we get,

[tex]\begin{gathered} (x-y)^3=(x-y)(x^2-2xy+y^2) \\ \text{ =}x(x^2-2xy+y^2)-y(x^2-2xy+y^2) \\ \text{ =}x^3-2x^2y+xy^2-yx^2+2xy^2-y^3 \\ \text{ =x}^3-y^3+3xy^2-3x^2y \end{gathered}[/tex]

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