Ejercicios interactivos: Factorización por agrupación

Desarrollo: 

$$ x^{2} + xy + ax + ay $$

$$ x \left(x + y \right) + a \left(x + y \right) $$

$$ \boxed{\left(x + a \right) \left(x + y \right)} $$

Desarrollo:

$$ xm + ym + xn + yn $$

$$ m \left(x + y \right) + n \left(x + y \right) $$

$$ \boxed{\left(m + n \right) \left(x + y \right)} $$

Desarrollo:

$$ 2am + 2ap – 3bm – 3bp $$

$$ 2a \left(m + p \right) – 3b \left(m + p \right) $$

$$ \boxed{\left(2a – 3b \right) \left(m + p \right)} $$

Desarrollo:

$$ 2x^{2}z – xyz + 10xz – 5yz $$

$$ xz \left(2x – y \right) + 5z \left(2x – y \right) $$

$$ \left(xz + 5z \right) \left(2x – y \right) $$

$$ z \left(x + 5 \right) \left(2x – y \right) $$

Desarrollo:

$$ x^{2} – a^{2} + x – a^{2}x $$

$$ x^{2} +  x – a^{2}x – a^{2} $$

$$ x \left(x + 1 \right) – a^{2} \left(x + 1 \right) $$

$$ \boxed{\left(x – a^{2} \right) \left(x + 1 \right)} $$

Desarrollo:

$$ 2x^{2} – 27 + 3x – 18x $$

$$ 2x^{2} + 3x – 18x – 27 $$

$$ x \left(2x + 3 \right) – 9 \left(2x + 3 \right) $$

$$ \left(x – 9\right) \left(2x + 3 \right) $$

Desarrollo: 

$$ 2m^{3} + 3m^{2} + 4m + 6 $$

$$ m^{2} \left(2m + 3 \right) + 2 \left(2m + 3 \right) $$

$$ \boxed{\left(m^{2} + 2 \right) \left(2m + 3 \right)} $$

Desarrollo:

$$ a^{2}x^{2} – 3bx^{2} + a^{2}y^{2} – 3by^{2} $$

$$ x^{2} \left(a^{2} – 3b \right) + y^{2} \left(a^{2} – 3b \right) $$

$$ \boxed{\left(x^{2} + y^{2} \right) \left(a^{2} – 3b \right)} $$

Desarrollo:

$$ 2xy + 3x + 6 + 4y $$

$$ 2xy + 3x + 4y  + 6 $$

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

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

Desarrollo:

$$ 5r – 4tz – rz + 20t $$

$$ 5r – rz + 20t – 4tz $$

$$ r \left(5 – z \right) + 4t \left(5 – z \right) $$

$$ \left(5 – z \right) \left(r + 4t \right) $$