Multiply following.
(a) (4x^{2}-x)(6-3x)
(b) (2x+6)^{2}
Solution
(a) (4x^{2} - x )(6 - 3x )
Again we will only FOIL this one out.
(4x^{2 } - x )(6 - 3x) = 24x^{2} -12x^{3} - 6x + 3x^{2} = -12x^{3} + 27 x^{2} - 6x
(b) (2x+6)^{2}
Now recall that 4^{2} = ( 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) = 4x^{2} + 12x + 12x + 36= 4x^{2 }+24x + 36
Following are example of some formula
( a + b ) ( a - b ) = a^{2} - b^{2}
( a + b )^{2} = a^{2} + 2ab + b^{2}
( a - b )^{2} = a^{2} - 2ab + b^{2}
Be careful to not make the following mistakes!
(a + b) ^{2 }≠ a^{2} + b^{2}
(a - b )^{2 } ≠ a^{2} - b^{2}
These are very common mistakes that students often make while they start first learning how to multiply polynomials.