Q. 4 E4.6( 5 Votes )

# Factories the following

x^{4} – 2x^{2}y^{2} + y^{4}

Answer :

In the given expression

1^{st} and last terms are perfect square

⇒ x^{4} = x^{2} × x^{2}

⇒ y^{4} = y^{2} × y^{2}

And the middle expression is in form of 2ab

2x^{2}y^{2} = 2 × x^{2} × y^{2}

∴ x^{2} × x^{2} - 2 × x^{2} × y^{2} + y^{2} × y^{2}

Gives (a-b)^{2} = a^{2}-2ab + b^{2}

⇒ x^{4} – 2x^{2}y^{2} + y^{4}

a = x^{2} and b = y^{2};

∴ x^{4} – 2x^{2}y^{2} + y^{4} = (x^{2} – y^{2}) (x^{2} + y^{2})

Hence the factors of x^{4} – 2x^{2}y^{2} + y^{4} are (x^{2} – y^{2}) and (x^{2} + y^{2})

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