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Fully factorize.

$x^2+x+\frac{1}{4}$

$x^2-\frac{2}{3}x+\frac{1}{9}$

$\left(a-b\right)x-\left(b-a\right)y$

$3\left(x+y\right)^3+27\left(x+y\right)^2$

$\left(a-b\right)^2-9b^2$

$\left(a-1\right)x^2+4\left(1-a\right)y^2$

$\left(3a+2b\right)^2-\left(-4a+b\right)^2$

$\left(a^2+b^2\right)^2-4a^2b^2$

Fully factorize.

$ax^2-\left(a+2\right)x+2$

$x^2-\left(a+1\right)x+a$

$ax^2+\left(2a-1\right)x-2$

$abx^2+\left(a+b\right)x+1$

$ax^2-\left(1+ab\right)x+b$

$abx^2+\left(2a^2-b^2\right)x-2ab$

Fully factorize.

$\left(x+y\right)^2+\left(x+y\right)-2$

$\left(a-b\right)^2-3\left(a-b\right)-10$

$\left(x+y\right)^2-4\left(x-y\right)^2$

$\left(x^2+x\right)^2+3\left(x^2+x\right)-10$

Fully factorize.

$a^2\left(x^2-a^2\right)-b^2\left(x^2-b^2\right)$

$2x^2-xy-y^2-7x+y+6$

$2x^2+xy-6y^2-4x-y+2$

$x^2-y^2-z^2+2yz$

$x-y-x^2+2xy-y^2+2$

$a^2b-2abc-b-ab^2+a-2c$

$x^3-\left(b-1\right)x^2+abx-ab\left(b-1\right)$

$a^2-ab+ac-2bc-2c^2$

$x^3+\left(a+2\right)x^2+\left(2a+1\right)x+a$

$x^3+3x^2y-3y-x$

$a^2b-ab^2-a^2c-ac^2-b^2c+bc^2+2abc$