Question

a^4+a^2b^2+b^4 factorize ​

Answer 1

Answer:

a^4 + a^2 b^2 + b^4

$(a ^{2} ) {}^{2} + (b ^{2} ) {}^{2} + a {}^{2} b {}^{2}$

Using the trigonometric identity:

$(x + y) {}^{2} = x {}^{2} + y {}^{2} + 2xy$

$x {}^{2} + y {}^{2} = (x + y) {}^{2} - 2xy$

$(a {}^{2} + b {}^{2} ) {}^{2} - 2a {}^{2} b {}^{2} + a {}^{2} b {}^{2}$

$(a {}^{2} + b {}^{2} ) {}^{2} - (ab) {}^{2}$

Using the trigonometric identity

x^2 - y ^2 = ( x+y) - (x-y)

a^4 + a^2b^2 +b^4 = (a^2+b^2 +ab) (a^2+b^2-ab)

Thus, the factorisation of the given expression is

(a^2 + b^2 + ab) (a^2 + b^2 - ab)

hope it will help you....