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Factorisation Using Algebraic Identities

vii Factorise...

Question

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

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Solution

We have $(x^{2} - 2 x y + y^{2}) - z^{2}$
$= [(x)^{2} - 2 \times x \times y + (y)^{2}] - z^{2}$
$= (x - y)^{2} - (z)^{2} [∵ (a - b)^{2} = a^{2} - 2 a b + b^{2}]$
$= (x - y - z) (x - y + z) [∵ a^{2} - b^{2} = (a - b) (a + b)]$

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Q. Question 2(vii)
Factorise

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

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Factorisation Using Algebraic Identities

Standard VIII Mathematics

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