Review: Factorisation

Factorization: Inverse of expansion (Distributive law)

Key terms

• Factor: Separated by multiplication. (e.g. 2ac has 3 factors: 2, a, and c)
• Terms: Separated by (+) or (-)
• GCF: Greatest common factor
• GCD: Greatest common division
• FOIL: First -Outer - Inner - Last

Difference of 2 quadratic terms:
4a² + 9x² = (2a)² + (3x)²

Perfect Quadratic Forms:
16y², while 16 is a quadratic number.
Another examples: 25x², 49g², 100x²y²


Factorize an Algebraic Form

ax + ay = a (x + y)

ax + ay = a (x + y)
a is the GCF of ax and ay
x is ax divided by a
y is ay divided by y

Example:
2a + 4
= 2a + 2 ● 2
= 2 (a + 2)

4x + 8
= 4x + 4 ● 2
= 4 (x + 2)

3a - 12
= 3a - 3 ● 4
= 3(a - 4)


16x² + 8x
= 8x (2x + 1)

4y - 2y²
= 2y (2 - y)

16x²y⁴z⁵ - 8x²y³z⁶
= 8x²y³z⁵ (2y - z)


Factorization by Grouping
Example:
2xy + 4x) + (3y + 6)
= 2x (y + 2) + 3 (y + 2)
= (2x + 3) (y + 2)

2xy + 4x² + 8 + 2y
= 2xy (1 + 2x) + 2 (4 + y)

or

2xy + 4x² + 8 + 2y
= 2 (xy + 2x²y + 4 + y)