(a) (4x2 - x )(6 - 3x )
Again we will only FOIL this one out.
(4x2 - x )(6 - 3x) = 24x2 -12x3 - 6x + 3x2 = -12x3 + 27 x2 - 6x
Now recall that 42 = ( 4)( 4)= 16 . Squaring with polynomials works the same way. Thus in this case we have,
( 2x + 6)2 = ( 2 x + 6) ( 2 x+ 6) = 4x2 + 12x + 12x + 36= 4x2 +24x + 36
Following are example of some formula
( a + b ) ( a - b ) = a2 - b2
( a + b )2 = a2 + 2ab + b2
( a - b )2 = a2 - 2ab + b2
Be careful to not make the following mistakes!
(a + b) 2 ≠ a2 + b2
(a - b )2 ≠ a2 - b2
These are very common mistakes that students often make while they start first learning how to multiply polynomials.