Factorization Of Algebraic Expressions — Maths STD 9 — Question
Gujarat BoardEnglish MediumSTD 9MathsFactorization Of Algebraic Expressions2 Marks
Question
Factorize:
$x^4+x^2 y^2+y^4$
✓
Answer
$x^4+x^2 y^2+y^4$
Adding $x^2 y^2$ and subtracting $x^2 y^2$ to the given equation
$=x^4+x^2 y^2+y^4+x^2 y^2-x^2 y^2$
$=x^4+2 x^2 y^2+y^4-x^2 y^2$
$=\left(x^2\right)^2+2 x x^2 \times y^2+\left(y^2\right)^2-(x y)^2$
Using the identity $(p+q)^2=p^2+q^2+2 p q$
$=\left(x^2+y^2\right)^2-(x y)^2$
Using the identity $p^2-q^2=(p+q)(p-q)$
$=\left(x^2+y^2+x y\right)\left(x^2+y^2-x y\right)$
$\therefore x^4+x^2 y^2+y^4=\left(x^2+y^2+x y\right)\left(x^2+y^2-x y\right)$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.