Question

Factorise x ^4+ y^4 + x²y²

Answer 1

Answer:

(x⁴+y⁴) - x²y²

(x²+y²)² = x⁴+y⁴+2x²y²

subtracting x²y² from both side

(x²+y²)² - x²y² = x⁴+y⁴+2x²y²-x²y²

=x⁴+y⁴+x²y²

Answer 2

Answer:$(x^2+xy+y^2)(x^2-xy+y^2)$

Two main factorization formulas

1. $x^2+2xy+y^2=(x+y)^2$
2. $a^2-b^2=(a+b)(a-b)$

Important : *It is an obvious fact that $x^2y^2=2x^2y^2-x^2y^2$*

Factorise $x^4+y^4+2x^2y^2-x^2y^2$

→ $x^4+2x^2y^2+y^4-x^2y^2$

→ $(x^2+y^2)-(xy)^2$ From 1

→ $(x^2+xy+y^2)(x^2-xy+y^2)$ From 2 (Difference of Perfect Square)