Q. 4 E4.6( 5 Votes )

# Factories the followingx4 – 2x2y2 + y4

In the given expression

1st and last terms are perfect square

x4 = x2 × x2

y4 = y2 × y2

And the middle expression is in form of 2ab

2x2y2 = 2 × x2 × y2

x2 × x2 - 2 × x2 × y2 + y2 × y2

Gives (a-b)2 = a2-2ab + b2

x4 – 2x2y2 + y4

a = x2 and b = y2;

x4 – 2x2y2 + y4 = (x2 – y2) (x2 + y2)

Hence the factors of x4 – 2x2y2 + y4 are (x2 – y2) and (x2 + y2)

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