Consider (a + b)(a² - ab + b²) = a³ + b³.
The binomial given above is called a Sum of Cubes since it is of the form a cube plus a cube.
To factor a sum of cubes:
To obtain binomial factor:
- Take a cube root of the first term, a³, of the binomial to get the first term ,a, of the binomial factor.
- Take a cube root of +b³ to get the last term of the binomial factor,+b.
To obtain the trinomial factor:
- Square the first term of the binomial factor to get first term of trinomial factor
- Take the opposite of the product of first and last term of binomial factor to obtain middle term of trinomial factor.
- Square the last term of the binomial factor to obtain the last term of the trinomial factor.
Cube rt Cube rt Sq a Opposite Product Sq b
a³ + b³ = (a + b) (a² - ab + b²)
Cube rt 2x Cube rt 3y Sq 2x opposite product Sq 3y
8x³ + 27y³ = (2x + 3y) ( 4x² - 6xy + 9y²)
Cube rt 5x Cube rt 2y Sq 5x opposite product Sq 2y
125x³ + 8y³ = (5x + 2y) ( 25x² - 10xy + 4y²)
