Multiply following.

(a) (4x²-x)(6-3x)

(b) (2x+6)²

Solution

 (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

 (b) (2x+6)²

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.