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(a+b)(a-b) Expansion and Visualisation

Faxtorise: ...

Question

Faxtorise: $(x^{2} - 2 x y + y^{2}) - z^{2}$

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Solution

$(x^{2} - 2 x y + y^{2}) - z^{2}$

$= (x - y)^{2} - z^{2}$ is of form $a^{2} - b^{2} = (a - b) (a + b)$

$= (x - y - z) (x - y + z)$

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\frac{x^{2} + y^{2} - z^{2} + 2 x y}{x^{2} - y^{2} - z^{2} - 2 y z} .

(x^{2} - 2 x y + y^{2}) - z^{2}

z^{2} - (x^{2} - 2 x y + y^{2})

Q. Factorisation of

z^{2} - (x^{2} + 2 x y + y^{2})

Factorise
$(x^{2} - 2 x y + y^{2}) - z^{2}$

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